The dynamics of electrons in doped quantum wells driven by terahertz radiation and a superlattice biased by an ac or dc voltage can be modeled. In simulations, we discover coherent, selfconsistent electron states, described by density matrix equations of motion, and dipole absorption spectra. The model simultaneously accounts for intersubband transitions and many nonlinear phenomena that have been observed in such systems. The simulations predict a bistable response for strong terahertz fields and bifurcations to coherent time-periodic quantum states. These bifurcation include, period-doubling bifurcations, producing a subharmonic response, Hopf  bifurcations producing an incommensurate frequency response, and a cascade of period doubling bifurcations to a strange attractor. One also observes a cascade of quasi-periodic orbits on the Hopf torus to a strange attractor. The theory, simulations and experiments describing these and other quantum phenomena will all be explored.