  The status of "ab initio" microscopic calculations of the 2H(p,gamma)3He and
3He(p,e+nu_e)4He reactions is reviewed. The methods used to generate accurate
nuclear ground- and scattering-state wave functions, and to construct realistic
electro-weak transition operators are described. The uncertainties in the
theoretical predictions, particularly those relevant to the p-3He weak capture,
are discussed. For the dp radiative capture, the theoretical results are
compared with the TUNL data in the energy range 0--100 keV.
