Air pollution abatement catalysis refers to catalytic technologies and processes for reducing emissions of environmentally unacceptable compounds. Major problems related to these catalytic clean-up technologies are mobile emission control, removal of nitrogen oxides (NOx), sulphur compounds, volatile organic compounds (VOCs) and other pollutants generated by industry or by other stationary sources. Application of the monolith catalysts and/or reactors is a key solution to these problems. This overview describes basic features of the monolithic structures and discusses their development and application prospects focusing on DeNO(x) catalysis. The status and ongoing modeling of the monolithic reactors are outlined. Particular emphasis is put on experimental validation and practical applications of the mathematical models of a monolithic reactor. (c) 2006 Elsevier B.V. All rights reserved.