An overview is provided on the computation of free energy changes in solution using perturbation theory, overlap sampling, and related approximate methods. As a specific application, extensive results are provided for free energies of hydration of substituted benzenes using the OPLS-AA force field in explicit TIP4P water. For a similar amount of computer time, the double-wide sampling and overlap sampling methods yield very similar results in the free-energy perturbation calculations. With standard protocols, the average statistical uncertainty in computed differences in free energies of hydration is 0.1 - 0.2 kcal/mol. Application of the power-series expansion in the Peierls equation was also tested. Use of the first-order term is generally reliable, while inclusion of the slowly-convergent, second-order fluctuation term causes deterioration in the results for strongly hydrogen-bonded solutes.