Right now they have no baseline compiler but will interpret (un-optimised?) LLVM IR at first, second tier is unoptimised LLVM compilation, then LLVM compilation with type recording hooks and finally a fully optimised compile. Given the history of the Unladed Swallow project and others using the LLVM JIT, they're likely to find they have a lot of work on their hands, particularly as PyPy is really rather good these days.
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There's some more technical details here: https://github.com/dropbox/pyston#technical-features
Right now they have no baseline compiler but will interpret (un-optimised?) LLVM IR at first, second tier is unoptimised LLVM compilation, then LLVM compilation with type recording hooks and finally a fully optimised compile. Given the history of the Unladed Swallow project and others using the LLVM JIT, they're likely to find they have a lot of work on their hands, particularly as PyPy is really rather good these days.
EDIT: There's some more info here in a post to the LLVM mailing list by one of the Pyston developers http://article.gmane.org/gmane.comp.compilers.llvm.devel/718.... They've added a simple escape analysis pass for GCed memory among other things.
As always, if you're interested in LLVM or compiler stuff you should subscribe to http://llvmweekly.org (disclaimer: I write it) and follow @llvmweekly