The development and the application of discovery process models have evolved to the point that these models now can be used to estimate the number of oil and gas fields remaining to be discovered in partially explored regions, and the rates at which fields will be discovered in the future. The fundamental data used to calibrate these models are taken from the systematic order that exists in the historical pattern of discovery in such regions (exploration plays, basins, provinces). The characteristic patterns of discovery vary from region to region, and ordinarily exhibit diminishing rates of return to wildcat drilling as a function of field size. The number of fields remaining to be discovered in each field-size class is estimated by a two stage procedure: direct nonlinea estimation of fields in the portion of the size distribution not truncated by economic factors (larger fields) and indirect estimating by using a relative frequency factor for the field-size classes in the economically truncated portion of the distribution (smaller fields). The forecast of the future rates of discovery then considers the total range of field sizes, on the basis of wildcat wells drilled, by applying the discovery process model to both segments of the estimated size distribution. The application of this procedure is illustrated for a variety of onshore and offshore exploration plays from different geologic environments that have different economic conditions (size truncation points).