The UCSC Repeat Browser contains data that is first mapped to hg19 or hg38 and then lifted to the consensus sequences (collectively called hg38reps) that make up the Repeat Browser. The datasets mapped include:

Mapping AlignmentsAlignments of each individual repeat instance in hg19 and hg38 back to the Repeat Browser consensus.
Mapping CoverageA coverage plot for the mapping alignments.
Conserved ElementsHighly conserved genomic sequences in vertebrates, placental mammals and primates lifted to the Repeat Browser.
RepeatMasker ProteinsProtein products of the repeat element as annotated in RepeatMasker records.
Other Cons AlnAlignment of all other Repeat Browser Consensuses against the currently viewed consensus.
Repeat Consensus AlignmentsAlignment of all repeats from the RepBase RepeatMasker Libraries
Tandem RepeatsDetected tandem sequence repeats within the consensus full-length repeat elements.
ENCODE TracksDNAse mapping, histone marks and TF ChIP-seq from ENCODE lifted to the Repeat Browser.
KZNF Tracks (Imbeault/Trono 2017 & Schmittges/Hughes 2016)Lifting of reprocessed data from large KZNF ChIP-seq screens.
TF Differentiation Data (Tsankov 2014)Lifting of large scale ChIP-seq dataset from differentiation time course across multiple cell types.
Stem Cell State Data (Theunissen 2016)Lifting of reprocessed data from primed and naïve human pluripotent stem cells.

Complete track descriptions are also available on the browser itself. All datasets can be viewed on the assembly they were mapped to, as well as the Repeat Browser.

Here are some standard files you may need to manipulate the Repeat Browser with other genomic tools:

All Sequences (fasta, one file): hg38reps.fa

2bit file: hg38reps.2bit

“Chromsome” sizes: hg38reps.sizes

liftOver files (from hg38): hg38_to_hg38reps.over.chain

liftOver files (from hg19): hg19_to_hg38reps.over.chain

RepeatMasker annotations (bed files for human genome assemblies)

hg38

hg19

All other files can be downloaded using the Table Browser feature and selecting the track of interest.  Alternatively you can poke around in these directories and download what you need. Also check the track descriptions to get a better idea of which file is which.

hg38reps directory

hg19 directory

hg38 directory

Source code: Repeat Browser Github