Atom transfer radical polymerization (ATRP) is one of the most extensively studied "living"/controlled radical polymerization (CRP) methods

not only owing to its simple

mild reaction conditions and broad applicability

but also it can be easily applied to produce polymeric materials with well-defined structure. In order to well understand and control the polymerization process

it is necessary to develop a comprehensive kinetic model for ATRP and coupling it with different reactor models

which can be useful for researchers to control over chain microstructure with predetermined molecular weight and narrow polydispersity

as well as copolymer composition and its composition distribution

and also optimize the polymerization conditions. This review illustrates the establishment of the appropriate ATRP kinetic model based on the theory of conventional free radical polymerization. Moreover

it also makes a comparison of the mechanism between "living"/controlled and conventional free radical polymerization examples in order to reveal the similarities and differences of the two methods within this field. In addition

we detail the research work concerning the kinetic modeling of ATRP

and more attention has been paid to analyze and summarize on the kinetic models from the point of different mathematical processing methods (method of moment

Monte Carlo simulation

and commercial software-PREDICI

GEPASI etc.).