© 2017 Wiley Periodicals, Inc. Molecular simulations of water using classical, molecular mechanic potential energy functions have enjoyed a 50-year history of development, and much has been learned regarding their parameterization and the essential physics that must be captured in order to reproduce water properties across the phase diagram and across system sizes, from the dimer to the condensed phase. While pairwise-additive force fields using fixed, point charge-based electrostatics have dominated this history owing to computational cost, their limitations in transferability are being recognized, owing particularly to the lack of many-body effects, as well as an inherent difficulty in capturing quantum mechanical effects that become important at short intermolecular separation. This has spurred an impressive development of novel functional forms and parameterization schemes to account for such effects, especially the leading many-body effect of polarization. This review discusses recent efforts in the development of advanced models of water, particularly with regard to important details of their parameterization from quantum mechanical or experimental data, the development of novel functional forms including machine learning-based models, and algorithms that reduce the computational cost of polarization dramatically, permitting them to potentially become competitive with pairwise-additive models as the standby of condensed-phase simulation. These technical developments are appraised based on their ability to impact numerical calculations on water, particularly the condensed phase, and it is hoped that this article provides a clear connection between the essential physics captured by the model and their fitness across a range of environments. WIREs Comput Mol Sci 2018, 8:e1355. doi: 10.1002/wcms.1355. This article is categorized under: Computer and Information Science > Computer Algorithms and Programming Molecular and Statistical Mechanics > Molecular Interactions Software > Simulation Methods.