Recent experimental investigations [20] of solid 4He have been interpreted as showing possible superfluidity in the solid at low temperatures, below 0.2 K. A solid behaving this way, exhibiting both long range translational order and superfluidity, has been called a supersolid phase. The existence of a supersolid phase was proposed many years ago [1], and has been discussed theoretically. In this paper we review simulations of the solid state of bulk 4He at or near absolute zero temperature by quantum Monte Carlo techniques. The techniques considered are variational calculations at zero temperature which use traditional Bijl-Dingle-Jastrow wavefunctions or more recently, shadow wavefunctions; Green's function Monte Carlo calculations at zero temperature; diffusion Monte Carlo, and finally, the finite temperature path integral Monte Carlo method. 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