Photoacoustic computed tomography (PACT) is an innovative biomedical imaging technique that has gained significant application in the field of biomedicine due to its ability to visualize optical contrast with high resolution and deep tissue penetration. However, the inherent challenges associated with photoacoustic signal excitation, propagation and detection often result in suboptimal image quality. To overcome these limitations, researchers have developed various advanced algorithms that span the entire image reconstruction pipeline. This review paper aims to present a detailed analysis of the latest advancements in PACT algorithms and synthesize these algorithms into a coherent framework. We provide tripartite analysis — from signal processing to reconstruction solution to image processing, covering a spectrum of techniques. The principles and methodologies, as well as their applicability and limitations, are thoroughly discussed. The primary objective of this study is to provide a thorough review of advanced algorithms applicable to PACT, offering both theoretical foundations and practical guidance for enhancing the imaging effect of PACT.