Several new types of regular and chaotic behavior of the parametrically driven pendulum are discovered with the help of computer simulations. A simple physical explanation is suggested to the phenomenon of subharmonic resonances. The boundaries of these resonances in the parameter space and the spectral composition of corresponding stationary oscillations are determined theoretically and verified experimentally. A close relationship between the upper limit of stability of the dynamically stabilized inverted pendulum and parametric resonance of the non-inverted pendulum is established. Most of the newly discovered modes are still waiting a plausible physical explanation.