In previous chapters, the free energy perturbation (FEP) and thermodynamic integration (TI) have been described as fundamental tools for calculating free energy differences, ΔF in complex systems. This chapter discusses alternative methods for calculating ΔF designed to outperform FEP and TI – “umbrella sampling” (Torrie & Valleau) and “Bennett’s acceptance ratio.” The “self-consistent histogram method” (Ferrenberg & Swendsen) for calculating entropy differences using MC is described for the Ising model. An important subject is the potential of mean force (PMF) which leads to free energy differences along a reaction coordinate; it is introduced and calculated for two hydrophobic particles approaching each other in water (Pangali et al.). A central method for calculating PMF is “the weighted histogram analysis method” (WHAM), which is described in detail following the original papers of Kumar et al. The success of WHAM has motivated many enhancements during the years, among them are the “multistate Bennett acceptance ratio” (MBAR) of Shirts and Chodera, “the statistical-temperature WHAM” (ST-WHAM (Fenwick), and “the umbrella integration method” (UIM) (Kästner & Thiel), which are discussed in some detail. The development in this field in the last 30 years is discussed with respect to methodology and the complexity of the specific systems studied.