Fourier transform ion cyclotron resonance (FT ICR) mass spectrometer offers highest resolving power and mass accuracy among all types of mass spectrometers. Its unique analytical characteristics made FT ICR important tool for proteomics, metabolomics, petroleomics, and investigation of complex mixtures. Signal acquisition in FT ICR MS takes long time (up to minutes). During this time ion–ion interaction considerably affects ion motion and result in decreasing of the resolving power. Understanding of those effects required complicated theory and supercomputer simulations but culminated in the invention of the ion trap with dynamic harmonization which demonstrated the highest resolving power ever achieved. In this review we summarize latest achievements in theory and simulation of FT ICR mass spectrometers. © 2014 Wiley Periodicals, Inc. Mass Spec Rev 35:219–258, 2016.