Classical electrostatics models that take into account polarization appeared as early as the 1950s. Barker in his 1953 paper "Statistical Mechanics of Interacting Dipoles" discussed the electrostatic energy of molecules in terms of "permanent and induced dipoles". 13 Currently, polarizable models generally fall into three categories: those based on induced point dipoles, 9, 14-23 the classical Drude oscillators, 24-26 and fluctuating charges. 27-30 More sophisticated force fields that are "electronic structure-based" 31, 32 or use "machine learning methods" 33 also exist, but incur higher computational costs. Discussions of the advantages and disadvantages of each model and their applications will be presented in the following sections. Compared to fixed charge models, the polarizable models are still in a relatively early stage. Only in the past decade or so has there been a systematic effort to develop general polarizable force fields for molecular modeling. A number of reviews have been published to discuss various aspects of polarizable force fields and their development. 9, 34-40 Here, we focus on the recent development and applications of different polarizable force fields. We begin with a brief introduction to the basic principles and formulae underlying alternative models. Next, the recent progress of several well-developed polarizable force fields is reviewed. Finally, applications of polarizable models to a range of molecular systems, including water and other small molecules, ion solvation, peptides, proteins and lipid systems are presented.