A review of recent theoretical calculations of blackbody radiation (BBR) shifts in optical atomic clocks is presented. We summarize previous results for monovalent ions that were obtained by a relativistic all-order single-double method, where all single and double excitations of the Dirac-Fock wave function are included to all orders of perturbation theory. A recently developed method for accurate calculations of BBR shifts in divalent atoms is then presented. This approach combines the relativistic all-order method and the configuration interaction method, which provides for accurate treatment of correlation corrections in atoms with two valence electrons. Calculations of the BBR shifts in B+, Al+, and In+ have enabled us to reduce the present fractional uncertainties in the frequencies of their clock transitions as measured at room temperature: to 4 x 10(-19) for Al+ and 10(-18) for B+ and In+. These uncertainties approach recent estimates of the limits of precision of currently proposed optical atomic clocks. We discuss directions of future theoretical developments for reducing clock uncertainties resulting from blackbody radiation shifts.