In the past decades, researchers/scientists have paid attention to the physical layer of underwater communications (UWCs) due to a variety of scientific, military, and civil tasks completed beneath water. This includes numerous activities critical for communication, such as survey and monitoring of oceans, rescue, and response to disasters under the sea. Till the end of the last decade, many review articles addressing the history and survey of UWC have been published which were mostly focused on underwater sensor networks (UWSN), routing protocols, and underwater optical communication (UWOC). This paper provides an overview of underwater acoustic (UWA) physical layer techniques including cyclic prefix orthogonal frequency division multiplexing (CP-OFDM), zero padding orthogonal frequency division multiplexing (ZP-OFDM), time-domain synchronization orthogonal frequency division multiplexing (TDS-OFDM), multiple input multiple output orthogonal frequency division multiplexing (MIMO-OFDM), generalized frequency division multiplexing (GFDM), unfiltered orthogonal frequency division multiplexing (UF-OFDM), continuous phase modulation orthogonal frequency division multiplexing (CPM-OFDM), filter bank multicarrier (FBMC) modulation, MIMO, spatial modulation technologies (SMTs), and orthogonal frequency division multiplexing index modulation (OFDM-IM). Additionally, this paper provides a comprehensive review of UWA channel modeling problems and challenges, such as transmission loss, propagation delay, signal-to-noise ratio (SNR) and distance, multipath effect, ambient noise effect, delay spread, Doppler effect modeling, Doppler shift estimation. Further, modern technologies of the physical layer of UWC have been discussed. This study also discusses the different modulation technology in terms of spectral efficiency, computational complexity, date rate, bit error rate (BER), and energy efficiency along with their merits and demerits.