Mastering real-time and accurate downhole information is crucial for ensuring drilling safety, improving drilling efficiency, and maximizing economic benefits. In recent years, logging while drilling (LWD) technologies, represented by mud pulse telemetry (MPT), achieved significant success. However, they still face challenges such as a large amount of downhole information conflicting with low information transmission rates, severe channel distortion, strong noise interference, and weak surface receiving signals. Therefore, this review collects and updates the papers, patents, and conference articles in the relevant field over the past ten years. Starting from the basic structure of communication systems, the downhole signal coding and modulation technologies of the MPT system are discussed. The attenuation reflection brought by the mud channel and various noise interferences in the system are described. The surface noise cancellation, channel equalization, synchronization, and decoding are studied in detail. By analyzing the theoretical principles, development breakthroughs, and relevant challenges that can improve the development of LWD technologies, this review aims to assist researchers in the field in obtaining the latest references and strategies.