Activated processes in materials are important for many of the properties that make them function. Batteries and catalysts are examples for which understanding how the component materials function on a timescale of milliseconds to seconds is critical to making improvements in a rational way. Modeling materials over these long timescales, relative to the timescale of atomic vibrations, is one of the grand challenges of the field. Transition state theory is central to bridging this timescale gap, and in the materials community, the harmonic approximation and the determination of saddle points to quantify reaction rates are ubiquitous. In this review, single- and double-ended methods for saddle point finding are discussed, as well as how finding saddle points can be used in the adaptive kinetic Monte Carlo method to model materials properties on the timescale of activated processes. Applications of surface diffusion and chemistry, phase boundary migration, and solid-solid phase transitions are presented.


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