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Significance: Photoacoustic computed tomography (PACT), a hybrid imaging modality combining optical excitation with acoustic detection, has rapidly emerged as a prominent biomedical imaging technique., Aim: We review the challenges and advances of PACT, including (1) limited view, (2) anisotropy resolution, (3) spatial aliasing, (4) acoustic heterogeneity (speed of sound mismatch), and (5) fluence correction of spectral unmixing., Approach: We performed a comprehensive literature review to summarize the key challenges in PACT toward practical applications and discuss various solutions., Results: There is a wide range of contributions from both industry and academic spaces. Various approaches, including emerging deep learning methods, are proposed to improve the performance of PACT further., Conclusions: We outline contemporary technologies aimed at tackling the challenges in PACT applications., (© 2024 The Authors.)