During the past decade dramatic progress has been made in calculating the binding energies of molecules. This is the result of two advances reported in 1989: an accurate method for solving the electronic Schrodinger equation that is applicable to a broad range of molecules-the CCSD(T) method-and families of basis sets that systematically converge to the complete basis set Limit-the correlation consistent basis sets. The former provides unprecedented accuracy for the prediction of a broad range of molecular properties, including molecular binding energies. The latter provides a means to systematically approach the complete basis set limit, i.e., the exact solutions of approximations to the Schrodinger equation. These two advances combined with a thorough analysis of the errors involved in electronic structure calculations lead to clear guidelines for ab initio calculations of binding energies, ranging from the strong bonds derived from chemical interactions to the extremely weak binding due to dispersion interactions. This analysis has also led to surprises, e.g., it has shown that the Moller-Plesset perturbation theory is unsuitable for calculation of bond energies to chemical accuracy, i.e., with errors of less that 1 kcal/mol. This applies whether one is interested in absolute bond energies or relative bond energies. Although the analysis presented here is focused on the calculation of molecular binding energies, this same approach can be readily extended to other molecular properties.