  Understanding the physical processes that regulate star formation and galaxy
evolution are major areas of activity in modern astrophysics. Nearby galaxies
offer unique opportunities to inspect interstellar medium (ISM), star formation
(SF), radiative, dynamic and magnetic physics in great detail from sub-galactic
(kpc) scales to sub-cloud (sub-pc) scales, from quiescent galaxies to
starbursts, and from field galaxies to overdensities. In this case study, we
discuss the major breakthroughs in this area of research that will be enabled
by the Atacama Large Aperture Submillimeter Telescope (AtLAST), a proposed 50-m
single-dish submillimeter telescope. The new discovery space of AtLAST comes
from its exceptional sensitivity, in particular to extended low surface
brightness emission, a very large 2 degree field of view, and correspondingly
high mapping efficiency. This paper focuses on four themes which will
particularly benefit from AtLAST: 1) the LMC and SMC, 2) extragalactic magnetic
fields, 3) the physics and chemistry of the interstellar medium, and 4) star
formation and galaxy evolution. With ~1000-2000h surveys each, AtLAST could
deliver deep dust continuum maps of the entire LMC and SMC fields at
parsec-scale resolution, high-resolution maps of the magnetic field structure,
gas density, temperature and composition of the dense and diffuse ISM in ~100
nearby galaxies, as well as the first large-scale blind CO survey in the nearby
Universe, delivering molecular gas masses for up to 10^6 galaxies (3 orders of
magnitude more than current samples). Through such observing campaigns, AtLAST
will have a profound impact on our understanding of the baryon cycle and star
formation across a wide range of environments.
