diff --git a/parquet/src/arrow/arrow_reader/mod.rs b/parquet/src/arrow/arrow_reader/mod.rs
index 7f68b07eb487..eea271306e25 100644
--- a/parquet/src/arrow/arrow_reader/mod.rs
+++ b/parquet/src/arrow/arrow_reader/mod.rs
@@ -2421,4 +2421,32 @@ mod tests {
         let a: &Float64Array = batch.column(2).as_any().downcast_ref().unwrap();
         assert_eq!(a.values(), &[42.000000, 7.700000, 42.125000, 7.700000]);
     }
+
+    #[test]
+    #[cfg(feature = "snap")]
+    fn test_read_nested_lists() {
+        let testdata = arrow::util::test_util::parquet_test_data();
+        let path = format!("{}/nested_lists.snappy.parquet", testdata);
+        let file = File::open(&path).unwrap();
+
+        let f = file.try_clone().unwrap();
+        let mut reader = ParquetRecordBatchReader::try_new(f, 60).unwrap();
+        let expected = reader.next().unwrap().unwrap();
+        assert_eq!(expected.num_rows(), 3);
+
+        let selection = RowSelection::from(vec![
+            RowSelector::skip(1),
+            RowSelector::select(1),
+            RowSelector::skip(1),
+        ]);
+        let mut reader = ParquetRecordBatchReaderBuilder::try_new(file)
+            .unwrap()
+            .with_row_selection(selection)
+            .build()
+            .unwrap();
+
+        let actual = reader.next().unwrap().unwrap();
+        assert_eq!(actual.num_rows(), 1);
+        assert_eq!(actual.column(0), &expected.column(0).slice(1, 1));
+    }
 }
diff --git a/parquet/src/column/reader/decoder.rs b/parquet/src/column/reader/decoder.rs
index b95b24a21c4b..da7fa78fe485 100644
--- a/parquet/src/column/reader/decoder.rs
+++ b/parquet/src/column/reader/decoder.rs
@@ -264,9 +264,13 @@ impl<T: DataType> ColumnValueDecoder for ColumnValueDecoderImpl<T> {
     }
 }
 
+const SKIP_BUFFER_SIZE: usize = 1024;
+
 /// An implementation of [`ColumnLevelDecoder`] for `[i16]`
 pub struct ColumnLevelDecoderImpl {
     decoder: Option<LevelDecoderInner>,
+    /// Temporary buffer populated when skipping values
+    buffer: Vec<i16>,
     bit_width: u8,
 }
 
@@ -275,9 +279,36 @@ impl ColumnLevelDecoderImpl {
         let bit_width = num_required_bits(max_level as u64);
         Self {
             decoder: None,
+            buffer: vec![],
             bit_width,
         }
     }
+
+    /// Drops the first `len` values from the internal buffer
+    fn split_off_buffer(&mut self, len: usize) {
+        match self.buffer.len() == len {
+            true => self.buffer.clear(),
+            false => {
+                // Move to_read elements to end of slice
+                self.buffer.rotate_left(len);
+                // Truncate buffer
+                self.buffer.truncate(self.buffer.len() - len);
+            }
+        }
+    }
+
+    /// Reads up to `to_read` values to the internal buffer
+    fn read_to_buffer(&mut self, to_read: usize) -> Result<()> {
+        let mut buf = std::mem::take(&mut self.buffer);
+
+        // Repopulate buffer
+        buf.resize(to_read, 0);
+        let actual = self.read(&mut buf, 0..to_read)?;
+        buf.truncate(actual);
+
+        self.buffer = buf;
+        Ok(())
+    }
 }
 
 enum LevelDecoderInner {
@@ -289,6 +320,7 @@ impl ColumnLevelDecoder for ColumnLevelDecoderImpl {
     type Slice = [i16];
 
     fn set_data(&mut self, encoding: Encoding, data: ByteBufferPtr) {
+        self.buffer.clear();
         match encoding {
             Encoding::RLE => {
                 let mut decoder = RleDecoder::new(self.bit_width);
@@ -305,12 +337,25 @@ impl ColumnLevelDecoder for ColumnLevelDecoderImpl {
         }
     }
 
-    fn read(&mut self, out: &mut Self::Slice, range: Range<usize>) -> Result<usize> {
+    fn read(&mut self, out: &mut Self::Slice, mut range: Range<usize>) -> Result<usize> {
+        let read_from_buffer = match self.buffer.is_empty() {
+            true => 0,
+            false => {
+                let read_from_buffer = self.buffer.len().min(range.end - range.start);
+                out[range.start..range.start + read_from_buffer]
+                    .copy_from_slice(&self.buffer[0..read_from_buffer]);
+                self.split_off_buffer(read_from_buffer);
+                read_from_buffer
+            }
+        };
+        range.start += read_from_buffer;
+
         match self.decoder.as_mut().unwrap() {
-            LevelDecoderInner::Packed(reader, bit_width) => {
-                Ok(reader.get_batch::<i16>(&mut out[range], *bit_width as usize))
+            LevelDecoderInner::Packed(reader, bit_width) => Ok(read_from_buffer
+                + reader.get_batch::<i16>(&mut out[range], *bit_width as usize)),
+            LevelDecoderInner::Rle(reader) => {
+                Ok(read_from_buffer + reader.get_batch(&mut out[range])?)
             }
-            LevelDecoderInner::Rle(reader) => reader.get_batch(&mut out[range]),
         }
     }
 }
@@ -323,41 +368,153 @@ impl DefinitionLevelDecoder for ColumnLevelDecoderImpl {
     ) -> Result<(usize, usize)> {
         let mut level_skip = 0;
         let mut value_skip = 0;
-        match self.decoder.as_mut().unwrap() {
-            LevelDecoderInner::Packed(reader, bit_width) => {
-                for _ in 0..num_levels {
-                    // Values are delimited by max_def_level
-                    if max_def_level
-                        == reader
-                            .get_value::<i16>(*bit_width as usize)
-                            .expect("Not enough values in Packed ColumnLevelDecoderImpl.")
-                    {
-                        value_skip += 1;
-                    }
-                    level_skip += 1;
-                }
-            }
-            LevelDecoderInner::Rle(reader) => {
-                for _ in 0..num_levels {
-                    if let Some(level) = reader
-                        .get::<i16>()
-                        .expect("Not enough values in Rle ColumnLevelDecoderImpl.")
-                    {
-                        // Values are delimited by max_def_level
-                        if level == max_def_level {
-                            value_skip += 1;
-                        }
-                    }
-                    level_skip += 1;
+        while level_skip < num_levels {
+            let remaining_levels = num_levels - level_skip;
+
+            if self.buffer.is_empty() {
+                // Only read number of needed values
+                self.read_to_buffer(remaining_levels.min(SKIP_BUFFER_SIZE))?;
+                if self.buffer.is_empty() {
+                    // Reached end of page
+                    break;
                 }
             }
+            let to_read = self.buffer.len().min(remaining_levels);
+
+            level_skip += to_read;
+            value_skip += self.buffer[..to_read]
+                .iter()
+                .filter(|x| **x == max_def_level)
+                .count();
+
+            self.split_off_buffer(to_read)
         }
+
         Ok((value_skip, level_skip))
     }
 }
 
 impl RepetitionLevelDecoder for ColumnLevelDecoderImpl {
-    fn skip_rep_levels(&mut self, _num_records: usize) -> Result<(usize, usize)> {
-        Err(nyi_err!("https://github.com/apache/arrow-rs/issues/1792"))
+    fn skip_rep_levels(&mut self, num_records: usize) -> Result<(usize, usize)> {
+        let mut level_skip = 0;
+        let mut record_skip = 0;
+
+        loop {
+            if self.buffer.is_empty() {
+                // Read SKIP_BUFFER_SIZE as we don't know how many to read
+                self.read_to_buffer(SKIP_BUFFER_SIZE)?;
+                if self.buffer.is_empty() {
+                    // Reached end of page
+                    break;
+                }
+            }
+
+            let mut to_skip = 0;
+            while to_skip < self.buffer.len() && record_skip != num_records {
+                if self.buffer[to_skip] == 0 {
+                    record_skip += 1;
+                }
+                to_skip += 1;
+            }
+
+            // Find end of record
+            while to_skip < self.buffer.len() && self.buffer[to_skip] != 0 {
+                to_skip += 1;
+            }
+
+            level_skip += to_skip;
+            if to_skip >= self.buffer.len() {
+                // Need to to read more values
+                self.buffer.clear();
+                continue;
+            }
+
+            self.split_off_buffer(to_skip);
+            break;
+        }
+
+        Ok((record_skip, level_skip))
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::encodings::rle::RleEncoder;
+    use rand::prelude::*;
+
+    fn test_skip_levels<F>(encoded: &[i16], data: ByteBufferPtr, skip: F)
+    where
+        F: Fn(&mut ColumnLevelDecoderImpl, &mut usize, usize),
+    {
+        let mut rng = thread_rng();
+        let mut decoder = ColumnLevelDecoderImpl::new(5);
+        decoder.set_data(Encoding::RLE, data);
+
+        let mut read = 0;
+        let mut decoded = vec![];
+        let mut expected = vec![];
+        while read < encoded.len() {
+            let to_read = rng.gen_range(0..(encoded.len() - read).min(100)) + 1;
+
+            if rng.gen_bool(0.5) {
+                skip(&mut decoder, &mut read, to_read)
+            } else {
+                let start = decoded.len();
+                let end = decoded.len() + to_read;
+                decoded.resize(end, 0);
+                let actual_read = decoder.read(&mut decoded, start..end).unwrap();
+                assert_eq!(actual_read, to_read);
+                expected.extend_from_slice(&encoded[read..read + to_read]);
+                read += to_read;
+            }
+        }
+        assert_eq!(decoded, expected);
+    }
+
+    #[test]
+    fn test_skip() {
+        let mut rng = thread_rng();
+        let total_len = 10000;
+        let encoded: Vec<i16> = (0..total_len).map(|_| rng.gen_range(0..5)).collect();
+        let mut encoder = RleEncoder::new(3, 1024);
+        for v in &encoded {
+            encoder.put(*v as _)
+        }
+        let data = ByteBufferPtr::new(encoder.consume());
+
+        for _ in 0..10 {
+            test_skip_levels(&encoded, data.clone(), |decoder, read, to_read| {
+                let (values_skipped, levels_skipped) =
+                    decoder.skip_def_levels(to_read, 5).unwrap();
+                assert_eq!(levels_skipped, to_read);
+
+                let expected = &encoded[*read..*read + to_read];
+                let expected_values_skipped =
+                    expected.iter().filter(|x| **x == 5).count();
+                assert_eq!(values_skipped, expected_values_skipped);
+                *read += to_read;
+            });
+
+            test_skip_levels(&encoded, data.clone(), |decoder, read, to_read| {
+                let (records_skipped, levels_skipped) =
+                    decoder.skip_rep_levels(to_read).unwrap();
+
+                // If not run out of values
+                if levels_skipped + *read != encoded.len() {
+                    // Should have read correct number of records
+                    assert_eq!(records_skipped, to_read);
+                    // Next value should be start of record
+                    assert_eq!(encoded[levels_skipped + *read], 0);
+                }
+
+                let expected = &encoded[*read..*read + levels_skipped];
+                let expected_records_skipped =
+                    expected.iter().filter(|x| **x == 0).count();
+                assert_eq!(records_skipped, expected_records_skipped);
+
+                *read += levels_skipped;
+            });
+        }
     }
 }
diff --git a/parquet/src/encodings/rle.rs b/parquet/src/encodings/rle.rs
index 9475275cb625..b0ae5af07d7f 100644
--- a/parquet/src/encodings/rle.rs
+++ b/parquet/src/encodings/rle.rs
@@ -338,6 +338,7 @@ impl RleDecoder {
     // These functions inline badly, they tend to inline and then create very large loop unrolls
     // that damage L1d-cache occupancy. This results in a ~18% performance drop
     #[inline(never)]
+    #[allow(unused)]
     pub fn get<T: FromBytes>(&mut self) -> Result<Option<T>> {
         assert!(size_of::<T>() <= 8);