Based on the energy conversion of light into sound, photoacoustic computed tomography (PACT) is an emerging biomedical imaging modality and has unique applications in a range of biomedical fields. In PACT, image formation relies on a process called acoustic inversion from received photoacoustic signals. While most PACT systems perform this inversion with a basic assumption that biological tissues are acoustically homogeneous, the community gradually realizes that the intrinsic acoustic heterogeneity of tissues could pose distortions and artifacts to finally formed images. This paper surveys the most recent research progress on acoustic heterogeneity correction in PACT. Four major strategies are reviewed in detail, including half-time or partial-time reconstruction, autofocus reconstruction by optimizing sound speed maps, joint reconstruction of optical absorption and sound speed maps, and ultrasound computed tomography (USCT) enhanced reconstruction. The correction of acoustic heterogeneity helps improve the imaging performance of PACT.