Mutations that lead to drug resistance limit the efficacy of antibiotics, antiviral drugs, targeted cancer therapies, and other treatments. Accurately calculating protein-drug binding affinity changes upon mutations in the drug target is of high interest as this can yield a better understanding into how such mutations drive drug-resistance, especially when the mutation in question does not directly interfere with binding of the drug. The main aim of this article is to provide an up-to-date reference on the computational tools that are available for the calculation of Gibbs energy (free energy) changes upon mutation, their strengths, and limitations. The methods that are discussed include free energy calculations (free energy perturbation, thermodynamic integration, multistate Bennett acceptance ratio), analysis of molecular dynamics simulations (linear interaction energy, molecular mechanics [MM]/Poisson-Boltzmann solvated area, and MM/generalized Born solvated area), and methods that involve quantum mechanical calculations (including QM/MM). The possibility to use machine learning is also introduced. Given that the benefit of accurately calculating binding affinity changes upon mutation depends on comparing calculated values with experimental measurements, a brief survey on experimental methods and observables is provided. Examples of computational studies that go beyond calculating the Gibbs energy changes are given. Factors that need to be addressed by the computational chemist and potential pitfalls are discussed at length.