Processes that promote the formation of dense cold clouds in the interstellar media of galaxies are reviewed. Those that involve background stellar mass include two-fluid instabilities, spiral density wave shocking, and bar accretion. Young stellar pressures trigger gas accumulation on the periphery of cleared cavities, which often take the form of rings by the time new stars form. Stellar pressures also trigger star formation in bright-rim structures, directly squeezing the pre-existing clumps in nearby clouds and clearing out the lower density gas between them. Observations of these processes are common. How they fit into the empirical star formation laws, which relate the star formation rate primarily to the gas density, is unclear. Most likely, star formation follows directly from the formation of cold dense gas, whatever the origin of that gas. If the average pressure from the weight of the gas layer is large enough to produce a high molecular fraction in the ambient medium, then star formation should follow from a variety of processes that combine and lose their distinctive origins. Pressurized triggering might have more influence on the star formation rate in regions with low average molecular fraction. This implies, for example, that the arm/interarm ratio of star formation efficiency should be higher in the outer regions of galaxies than in the main disks.