The Square Kilometre Array (SKA) will transform our understanding of the role of the cold, atomic gas in galaxy evolution. The interstellar medium (ISM) is the repository of stellar ejecta and the birthsite of new stars and, hence, a key factor in the evolution of galaxies over cosmic time. Cold, diffuse, atomic clouds are a key component of the ISM, but so far this phase has been diffcult to study, because its main tracer, the HI 21 cm line, does not constrain the basic physical information of the gas (e.g., temperature, density) well. The SKA opens up the opportunity to study this component of the ISM through a complementary tracer in the form of low-frequency (<350 MHz) carbon radio recombination lines (CRRL). These CRRLs provide a sensitive probe of the physical conditions in cold, diffuse clouds. The superb sensitivity, large field of view, frequency resolution and coverage of the SKA allows for efficient surveys of the sky, that will revolutionize the field of low-frequency recombination line studies. By observing these lines with the SKA we will be able determine the thermal balance, chemical enrichment, and ionization rate of the cold, atomic medium from degree-scales down to scales corresponding to individual clouds and filaments in our Galaxy, the Magellanic Clouds and beyond. Furthermore, being sensitive only to the cold, atomic gas, observations of low-frequency CRRLs with the SKA will aid in disentangling the warm and cold constituents of the HI 21 cm emission.Advancing Astrophysics with the Square Kilometre Array