The interstellar medium (ISM) mediates galactic evolution as the reservoir of material for future star formation and the repository of energy and matter output by stellar processes. It consists of matter (both gas and dust), magnetic fields, and relativistic particles in rough equipartition in energy density. Understanding this equilibrium requires observing the discrete thermally-stable phases as well as tracing the phase transitions and turbulence that mix the phases and produce unstable gas. The heating, cooling, and ionization of the ISM trace the flow of radiation through galaxies, so the impact of the ISM must be understood to interpret observations of most astrophysical phenomena. Canadians have played leading roles in ISM science for decades. The Canadian user community for the Dominion Radio Astrophysical Observatory (DRAO) Synthesis Telescope designed and completed the Canadian Galactic Plane Survey (CGPS). The CGPS identified a wealth of small-scale structure in H I emission as well as self-absorption and in the structure of polarized emission. These observations demonstrated that no phase of the ISM, including the transition from atomic gas to star formation, can be understood in isolation. Canadians have also played leading roles in the characterization of dust with Planck and balloon-borne telescopes. Canadians have also used pulsar scintillometry to measure structure in the ISM at the smallest scales, below 1 AU. The 2020s offer many opportunities for ISM science in Canada. A major but cost-effective upgrade to the Synthesis Telescope with broadband (400--1800 MHz) single-pixel feeds would enable broadband polarimetry as well as wide-area, arcminute surveys of radio recombination line emission tracing ionized gas that cannot be observed in any other way. The next generation of balloon-borne telescopes will investigate magnetic fields and dust properties in a wide range of regions. Large single dishes remain essential for our understanding of the diffuse structure which characterizes the ISM. The Green Bank Telescope is the only facility available to Canadians capable of observing the range of molecular transitions from 1--116 GHz. Very long baseline interferometry (VLBI) capability enables parallax measurements of pulsars and masers, needed for measuring the structure of the Galaxy and the ISM within it, and for further progress in scintillometry. Canadian ISM astronomers will continue to participate in cosmological experiments including CHIME and CHORD. Protecting quiet radio frequency interference environments at radio observatories will be ever more important as broadband observations are ever more central to ISM spectral line and continuum science. Computational capability is essential both for numerical work and for handling the observational data. White paper identifier W044
