One-step amination of long-chain fatty alcohols with dimethylamine for commercial production of tertiary amines, RNMe2 (R = C8 - C22), is one of the key reactions for the oleo and detergents industries producing fatty alcohols. This reaction has been reviewed using related patents and articles published in the last four decades to gain an understanding of the current situation and future outlook. In particular, as many as possible related Chinese articles written in Chinese have been included because progress in and the basic concepts of one-step aminations in China have remained unknown because of the language barrier, and because the program was supported by the 7th (1986-1990) and 9th (1996-2000) five-year national projects in China. The basic concepts of amination catalysts developed by the major researchers worldwide have been compared. On the basis of this literature review, the following topics have been considered and discussed: catalyst development for the commercial production of tertiary amines, global competition in developing the ultimate production process, the basic functions of amination catalysts, the basic concepts of future superactive catalysts that could function at Cu-concentrations of 10-20 ppm, and the catalytic systems with the best potential. Current amination technology has matured since around 2000. The present review has therefore been prepared as an introduction to new concepts for the development of future advanced catalysts and production processes.