Laser Interferometer Space Antenna (LISA) will be a transformative experiment
for gravitational wave astronomy as it will offer unique opportunities to
address many key astrophysical questions in a completely novel way. The synergy
with ground-based and other space-based instruments in the electromagnetic
domain, by enabling multi-messenger observations, will add further to the
discovery potential of LISA. The next decade is crucial to prepare the
astrophysical community for LISA's first observations. This review outlines the
extensive landscape of astrophysical theory, numerical simulations, and
astronomical observations that are instrumental for modeling and interpreting
the upcoming LISA datastream. To this aim, the current knowledge in three main
source classes for LISA is reviewed: ultra-compact stellar-mass binaries,
massive black hole binaries, and extreme or intermediate mass ratio inspirals.
The relevant astrophysical processes and the established modeling techniques
are summarized. Likewise, open issues and gaps in our understanding of these
sources are highlighted, along with an indication of how LISA could help make
progress in the different areas. New research avenues that LISA itself, or its
joint exploitation with studies in the electromagnetic domain, will enable, are
also illustrated. Improvements in modeling and analysis approaches, such as the
combination of numerical simulations and modern data science techniques, are
discussed. This review is intended to be a starting point for using LISA as a
new discovery tool for understanding our Universe.