Reservoir pressure plays a significant role in all reservoir and production engineering studies. It is crucial to characterize petroleum reservoirs: by detecting fluid movement, computing oil in place, and calculating the recovery factor. Knowledge of reservoir pressure is essential for predicting future production rates, optimizing well performance, or planning enhanced oil recovery strategies. However, applying the methods to investigate reservoir pressure performance is challenging because reservoirs are large, complex systems with irregular geometries in subsurface formations with numerous uncertainties and limited information about the reservoir's structure and behavior. Furthermore, many computational techniques, both numerical and analytical, have been utilized to examine reservoir pressure performance. This paper summarizes the concepts and applications of traditional and novel ways to investigate reservoir pressure changes over time. It provides a comprehensive review that assists the reader in recognizing and distinguishing between various techniques for obtaining an accurate description of reservoir pressure behavior during production, such as the reservoir simulation method, material balance equation approach, time-lapse seismic data, and modern artificial intelligence methods. Thus, the central concept of these procedures and a list of the authors' research are discussed.