The Laser Interferometer Space Antenna (LISA) will allow the detection of gravitational wave signals from a strikingly large variety of sources, ranging from stellar-mass binaries in our own galaxy to mergers between nascent massive black holes at high redshift. LISA is expected to revolutionize our understanding of these astrophysical sources by allowing reconstruction of their demographics and dynamical evolution, as well as discovery of new types of sources, including some that have been theorized but not yet detected by conventional means. Overall, LISA observations of Galactic binaries will address many open questions in stellar astrophysics, such as the evolution of binary star systems, the origin of different transient phenomena, the origin of the elements and even the structure of the Galaxy. LISA will open up a wide discovery space for black holes. The observed black hole mass spectrum will span ten orders of magnitude, ranging from a few times the mass of our Sun for stellar-mass black holes up to hundreds of billions solar masses for the most extreme massive black holes. LISA will also be able to observe the inspiral of a compact object such as a stellar-mass black holes, a neutron stars or a white dwarf onto a massive black holes residing in galactic centers. Because of the difference in mass between the massive black hole and the few–tens of solar masses of the compact object, these events are called extreme mass-ratio inspirals (EMRIs). From the astrophysical perspective, these are potentially the most exciting class of sources in the LISA band. Finally, the joint exploitation of LISA data with data from terrestrial gravitational wave detectors and electromagnetic observations across essentially all possible wavelengths, from infrared and radio to X-ray and gamma-rays, will further enhance its astrophysical impact.