Underwater acoustic communications face significant challenges unprecedented in radio terrestrial communications including long multipath delay spreads, strong Doppler effects, and stringent bandwidth requirements. Recently, multi-carrier communications based on orthogonal frequency division multiplexing (OFDM) have seen significant growth in underwater acoustic (UWA) communications, thanks to their well well-known robustness against severely time-dispersive channels. However, the performance of OFDM systems over UWA channels significantly deteriorates due to severe intercarrier interference (ICI) resulting from rapid time variations of the channel. With the motivation of developing enabling techniques for OFDM over UWA channels, the major contributions of this thesis include (1) two effective frequencydomain equalizers that provide general means to counteract the ICI; (2) a family of multiple-resampling receiver designs dealing with distortions caused by user and/or path specific Doppler scaling effects; (3) proposal of using orthogonal frequency division multiple access (OFDMA) as an effective multiple access scheme for UWA communications; (4) the capacity evaluation for single-resampling versus multiple-resampling receiver designs. All of the proposed receiver designs have been verified both through simulations and emulations based on data collected in real-life UWA communications experiments. Particularly, the frequency domain equalizers are shown to be effective with significantly reduced pilot overhead and offer robustness against Doppler and timing estimation errors. The multiple-resampling designs, where each branch is tasked with the Doppler distortion of different paths and/or users, overcome the disadvantages of the commonly-used single-resampling receivers and yield significant performance gains. Multiple-resampling receivers are also demonstrated to be necessary for UWA OFDMA systems. The unique design effectively mitigates interuser interference (IUI), opening up the possibility to exploit advanced user subcarrier assignment schemes. Finally, the benefits of the multiple-resampling receivers are further demonstrated through channel capacity evaluation results.