Transmission over the noncoherent additive white Gaussian noise channel is considered, where the transmitted signal undergoes a phase rotation, unknown to the transmitter and the receiver. The effects of phase dynamics are explicitly taken into account by considering a block-independent model for the phase process: the unknown phase is constant for a block of N complex symbols and independent from block to block. In the first part of the paper, a summary of the analytic results on related work regarding the capacity achieving input distribution is presented, followed by some numerical and asymptotic results. In the second part of this paper, inspired by the capacity results, two classes of coding and modulation schemes are proposed for fast and moderate phase dynamics. Due to the complexity issues, these two cases are treated separately. In the first case, serially concatenated turbo codes are utilized, while in the second, irregular low-density parity-check codes are used in conjunction with channel-matched modulation schemes. Simulation results show that these codes can achieve close-to-capacity performance with moderate complexity, and outperform the best known codes so far.