Find rsIDs for GRCh37 SNPs and rsIDs for GRCh38 SNPs and compare for overlap I have a long list of variant IDs that I generated as a result of research done one GRCh37 genomes (e.g. 13_28025615_G_C_b37). I want to get their rsIDs and compare them to a newly-obtained list of GRCh38 rsIDs that have also been retrieved from similarly formatted variant IDs (e.g. chr22_50473581_G_A_b38). How would I go about doing this? I've tried installing biomaRt as a package but I can't quite make heads or tails of it and it's not clear to me that it would support both versions of genome builds.
it's not clear to me that it would support both versions of genome
  builds.


You can specify what version of the database you are querying.

I'd start with biomart on the ensembl website, see if you can get it to do what you want, then work on getting biomaRt to do what you want.