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-wave sources of undisclosed parameters. Participants are asked to analyze the data sets and report the maximum information about source parameters. The challenges are being released in rounds of increasing complexity and realism, and so far they have already demonstrated the recovery of model signals from supermassive black-hole binaries, from ~20,000 overlapping Galactic white-dwarf binaries, and from the extreme--mass-ratio inspirals of compact objects into central galactic black holes. Here we discuss the results of Challenge 1B (a second entry point into the Challenges for groups new to LISA data analysis) and we present Challenge 3, which includes chirping Galactic binaries, spinning black-hole inspirals, more EMRIs, bursts from cosmic-string cusps, and primordial stochastic backgrounds.