Photoacoustic computed tomography (PACT) is a rapidly developing biomedical imaging modality and has attracted substantial attention in recent years. Image reconstruction from photoacoustic projections plays a critical role in image formation in PACT. Here we review six major classes of image reconstruction approaches developed in the past three decades, including delay and sum, filtered back projection, series expansion, time reversal, iterative reconstruction, and deep-learning-based reconstruction. The principal ideas and implementations of the algorithms are summarized, and their reconstruction performances under different imaging scenarios are compared. Major challenges, future directions, and perspectives for the development of image reconstruction algorithms in PACT are also discussed. This review provides a self-contained reference guide for beginners and specialists in the photoacoustic community, to facilitate the development and application of novel photoacoustic image reconstruction algorithms.