The future space-based gravitational-wave detector LISA will deliver rich and information-dense data by listening to the milliHertz Universe. The measured time series will contain the imprint of tens of thousands of detectable Galactic binaries constantly emitting, tens of supermassive black hole merger events per year, tens of stellar-origin black holes, and possibly thousands of extreme mass-ratio inspirals. On top of that, we expect to detect the presence of stochastic gravitational wave backgrounds and bursts. Finding and characterizing many such sources is a vast and unsolved task. The LISA Data Challenges (LDCs) are an open and collaborative effort to tackle this exciting problem. A new simulated data set, nicknamed Sangria, has just been released with the purpose of tackling mild source confusion with idealized instrumental noise. This presentation will describe the LDC strategy, showcase the available datasets and analysis tools, and discuss future efforts to prepare LISA data analysis.