A general theory is proposed for the rate of nucleation of solid or liquid phases in solid or liquid solutions at different pressures. It is found that higher pressures inhibit or stimulate the nucleation process when the partial molecular volume of solute is, respectively, larger or smaller in the nucleating phase than in the solution. The general description is applied to nucleation in liquid solutions in pores or droplets. The analysis shows that when the solute partial molecular volume is larger in the nucleating phase than in the solution, the nucleation rate is higher for pore-trapped solution with a concave meniscus than for the corresponding bulk solution, but it is lower if the meniscus is convex or if the solution is dispersed into droplets. The effect of pressure and of pore or droplet size on the critical supersaturation for the onset of nucleation is also analyzed.