High performance acoustic underwater communications require high bandwidths for high data rates, low carrier frequencies for low channel attenuation and highly directive transducers. These at first sight contradictory requirements can be satisfied by employing parametric arrays. In this way highly directive radiation, which mitigates multipath and thus reduces delay and Doppler spread, of low frequency waves of large relative bandwidth can be achieved by small transducers of small relative bandwidth. Scientific challenges beyond the power loss of the nonlinear signal conversion arise from the inherent nonlinear signal distortions of parametric transmission. From the physical modeling it is shown that the parametric underwater channel can be modeled as a concatenation of a static nonlinear system and a dynamic linear system. The relevant part of the nonlinear system is mainly quadratic. Based on this system model we study modulation techniques which allow for high performance data transmission over nonlinear communication channels.