I'm not aware of any major breakthroughs in the past few years, but lead-free solder alloys are an active research area right now. Here's a SANDIA report from 2012 that has some context and some cool micrographs; you can find lots more by searching the web for tin whisker growth in lead-free solders.

(edit: pdf warning) http://prod.sandia.gov/techlib/access-control.cgi/2012/12051...