The Direct Statistical Approach (DSA) was developed in the 1980s and 1990s to optimize Monte Carlo deep penetration (fixed-source) radiation transport calculations. It is based on a detailed mathematical approach to the splitting and Russian roulette problem, independent of, or dependent on, the weight of the particle track. As it relies on splitting and Russian roulette, it is of quite general application and has been employed on a wide variety of problems: reactor shielding, accelerator shielding, accelerator-driven systems, dosimetry, and nuclear medicine. The development of the DSA culminated in the inclusion of a multiresponse capability. Over the last 10 years this capability has completely supplanted the single-response version of the DSA. It is considered that the multiresponse capability represents a significant advance. Examples of its use are illustrated. The DSA is currently undergoing a substantial update. The state of the art of the new code is given.