The spin dynamics and the orbital dynamics in the A and B phases of superfluid $^3$He are analyzed. Attention is focused on solitons and instantons: nonsingular configurations of the field of the order parameter of the $^3$He superfluid phases. A qualitative explanation in terms of solitons and instantons is offered for several experiments involving the A and B phases of $^3$He. The analysis of these questions is prefaced by some general information on the order parameter and the free energy in superfluid $^3$He.