Abstract Thermal maturity modeling is now a highly developed discipline, with a number of excellent software programs available for working geologists. Maturity models are used to describe the behavior of individual thermal indicators (such as various biomarkers and vitrinite reflectance), as well as hydrocarbon generation and cracking. Maturity modeling must begin with a valid conceptual model of local geology, and should then follow a logical sequence. First, present-day heat flow and thermal conductivities are selected to predict correctly the observed present-day temperatures. Next, paleoheat flows and the magnitudes of depositional and erosional events are chosen to agree with the regional geology and concepts of basin evolution and to predict correctly the observed values for any available thermal indicators. Finally, modeling of hydrocarbon generation within a source rock and cracking of oil to gas in source or reservoir rocks is carried out once all input data are internally consistent (optimized). Kinetic models for organic maturation are clearly superior to the time^temperature index (TTI) approach and should therefore be used in future applications. Some kinetic models now predict hydrocarbon expulsion as well as generation and thus may provide more accurate estimates of hydrocarbon composition than generation models alone. Faulting and other tectonic complexities remain problems. One-dimensional maturity modeling (z spatial dimension plus time) seems adequate for most exploration applications.