The good correlation that is observed in local spiral galaxies between the molecular gas surface density and the star formation rate surface density demonstrates that there is a close connection between the presence of molecular gas and the formation of stars. However, the nature of this connection remains a matter of some debate. Does efficient star formation require the cooling provided by carbon monoxide (CO) and other heavy molecules? Or are they simply good tracers of conditions conducive to star formation? In this talk, I will discuss the role that molecules such as CO play in governing the thermal balance of interstellar gas and present the results of some recent simulations designed to explore the connection between molecular gas and star formation.