We discuss a fully nonlinear interfacial formulation of internal gravity waves in three dimensions. The horizontal two-fluid system has either a finite depth, or one or both of the layers may be infinitely deep. Along the horizontal top or bottom, a variable topography may be present. Various successive approximations of the mathematical method are illustrated by numerical calculations. Motivated by solitary waves of very large amplitude, we calculate these waves, with amplitude up to almost the maximum possible, using even a quadratic approximation of the nonlinear-numerical scheme. For example, for depth ratio 1:20.4 we calculate solitary waves of amplitude 9.4. Various three-dimensional patterns are illustrated. The theoretical-numerical waves are compared to experiments and field observations.