Recent advances on the analytical form of the hydrodynamic force and heat/mass transfer from a particle, bubble, or drop are examined critically. Also some of the recent computational studies, which help strengthen or clarify our knowledge of the complex velocity and temperature fields associated with the momentum and heat/mass transfer processes are also mentioned in a succinct way. Whenever possible, the processes of energy/mass exchange and of momentum exchange from spheres and spheroids are examined simultaneously and any common results and possible analogies between these processes are pointed out. This approach results in a better comprehension of the transport processes, which are very similar in nature, as well as in the better understanding of the theoretical expressions that are currently used to model these processes. Of the various terms that appear in the transient equations, emphasis is given to the history terms, which are lesser known and more difficult to calculate. The origin, form, and method of computation of the history terms are pointed out as well as the effects of various parameters on them. Among the other topics examined here are the differences in the governing and derived equations resulting by finite Reynolds and Peclet numbers; the origin, theoretical validity and accuracy of the semi-empirical expressions; the effects of finite internal viscosity and conductivity of the sphere; the effects of small departures from the spherical shape; the effects of the finite concentration; and the transverse, or lift, components of the force on the sphere.