Do we understand the 22-year solar activity cycle?

After a brief review of the most important observational facts of the solar activity cycle, the basic mechanisms which are thought to be responsible for cycle generation are described with particular reference to the fundamental equations of magnetohydrodynamics. The empirical Babcock's model is illustrated as an instructive example introductory to the modern α-ω dynamo theories of the solar cycle, based on the mutual interaction of rotation with convection and magnetic fields. Different classes of α-ω dynamo theories operating in the convection zone are analyzed, starting from linear or kinematic dynamos, based on mean field electrodynamics, and ending with the description of fully hydromagnetic dynamos in which all the magnetohydrodynamical equations are numerically solved at once. The most recent efforts for modelling the boundary layer dynamos are also discussed. Conclusions are moderately optimistic.