Far-infrared and submillimeter observations have established the fundamental role of dust-obscured star formation in the assembly of stellar mass over the past similar to 12 billion years. At z = 2-4, the so-called "cosmic noon", the bulk of star formation is enshrouded in dust, and dusty star-forming galaxies (DSFGs) contain similar to 50% of the total stellar mass density. Star formation occurs in dense molecular clouds, and is regulated by a complex interplay between all the ISM components that contribute to the energy budget of a galaxy: gas, dust, cosmic rays, interstellar electromagnetic fields, gravitational field, and dark matter. Molecular gas is the actual link between star-forming gas and its complex environment: much of what we know about star formation comes from observations of molecular line emissions. They provide by far the richest information about the star formation process. However, their interpretation requires complex modeling of the astrochemical networks which regulate molecular formation and establish molecular abundances in a cloud, and a modeling of the physical conditions of the gas in which molecular energy levels become populated. This paper critically reviews the main astrochemical parameters needed to obtain predictions about molecular signals in DSFGs. Molecular lines can be very bright compared to the continuum emission, but radiative transfer models are required to properly interpret the observed brightness. We review the current knowledge and the open questions about the interstellar medium of DSFGs, outlining the key role of molecular gas as a tracer and shaper of the star formation process.
