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Cosmic rays alter the chemistry and dynamics of the molecular gas that collapses to form young stellar systems. They enable a rich chemistry to take place during the process of star formation, affecting the thermodynamics of the gas, and yielding a wealth of observable tracers. The gas flow and density structures are also affected, because the coupling to the magnetic field depends on the ionization state of the gas. Despite this, their abundance, particularly in denser regions, remains uncertain. Although cosmic rays in distant locations are not directly observable, we can infer their presence in molecular clouds from chemical tracers of gas ionization, gamma ray and synchrotron emission and enhanced gas temperature. I will discuss how these observations can be used to constrain models of cosmic ray acceleration and transport. I will give an overview of the different transport regimes thought to play a role (ballistic propagation, diffusion, and self-modulation), and what predictions these make for the variation of the ionization rate with gas density. As the transport of cosmic rays is influenced by the properties of small-scale turbulence, I will discuss some recent work I've done on the damping of turbulence in the interstellar medium due to radiative cooling.