  Line intensity mapping (LIM) is a promising approach to study star formation
and the interstellar medium (ISM) in galaxies by measuring the aggregate line
emission from the entire galaxy population. In this work, we develop a simple
yet physically-motivated framework for modeling the line emission as would be
observed in LIM experiments, which is done by building on analytic models of
the Cosmic Infrared Background that connect total infrared luminosity of
galaxies to their host dark matter halos. We present models of the HI 21cm,
CO(1-0), [C II] 158$\mu$m, and [N II] 122 and 205$\mu$m lines consistent with
current observational constraints. With four case studies of various
combinations of these lines that probe different ISM phases, we demonstrate the
potential for reliably extracting physical properties of the ISM, and the
evolution of these properties with cosmic time, from auto and cross-correlation
analysis of these lines as measured by future LIM experiments.
