At any one moment, LISA will be sensing gravitational waves from millions of individual sources. The vast majority of these will be binary systems of compact objects in the Milky Way, but signals will also be received from extragalactic sources such as the mergers of massive black holes. Each of these signals has a distinct waveform that depends on the astrophysical properties of the source (masses, spins, orientations, positions, etc.). Thanks to extensive work in theory and modeling, we have very good templates for these sources which we can compare to the LISA data and extract individual signals using a technique known as matched filtering. The entire LISA data set is processed as a hierarchical global fit, where individual sources are added and subtracted to improve the overall fit. The most significant sources are easily identified and characterized. As the signal strength decreases, a point is eventually reached where no additional sources can be confidently extracted. Simulations with mock LISA data suggest that tens of thousands of individual signals will be identified in the full LISA data set with the remaining Milky Way binaries producing an unresolved, but still detected, foreground of gravitational waves in the lower part of the LISA sensitivity band. The LISA community is continuing to conduct mock data challenges of increasing sophistication to hone the data analysis techniques that will be used to solve this problem.