The Mock LISA data challenges are a program to demonstrate LISA data-analysis capabilities and to encourage their development. Each round of challenges consists of several data sets containing simulated instrument noise and gravitational waves from sources of undisclosed parameters. Participants are asked to analyze the data sets and report the maximum information about the source parameters. The challenges are being released in rounds of increasing complexity and realism: here we present the results of Challenge 2, issued in Jan 2007, which successfully demonstrated the recovery of signals from nonspinning supermassive-black-hole binaries with optimal SNRs between \10 and 2000, from \20\ 000 overlapping galactic white-dwarf binaries (among a realistically distributed population of 26 million), and from the extreme-mass-ratio inspirals of compact objects into central galactic black holes with optimal SNRs \100.