It's possible to run R just from a prompt, which works well for individual commands but isn't great for editing those commands or keeping track of what you did. Looking around, I found that there is (of course!) a Vim-R plugin available, so I gave it a try - and really liked it! It is enabled for files ending in .R or .Rmd and allows you to launch an R prompt and run one or many lines in that prompt directly from vim.
The .Rmd format is actually for R Markdown, which is a markdown format that lets you embed R. I've been using it as a sort of lab book to keep track of what I did and why. You can then generate a document with all the R code shown and evaluated - very neat!