In this review, we have systematically discussed diesel particulate composition and its formation, understanding of which is essential to design the effective catalyst compositions. The most commonly used after treatment strategies such as diesel oxidation catalysts, diesel particulate filters, and partial flow filters are described followed by chronological and category-wise discussions on various groups of reported soot oxidation catalysts. A detailed review is also presented on mechanistic and kinetics aspects of non-catalytic direct particulate matter (PM) or soot oxidation in air/O-2 and NO2. Recent progress in catalyst development with a focus on the low-cost catalyst for diesel PM oxidation has been given more emphasis considering their renewed importance.