Photoacoustic computed tomography (PACT) has become a promising imaging modality from laboratory to clinical research. Of many components of PACT system, the ultrasound (US) array transducer is an essential device to simultaneously receive photoacoustic (PA) signals from several directions in a parallel manner. Many research groups and companies have developed various types of US array transducers while accounting the properties of the PA waves to achieve better image quality, deeper imaging depth, faster imaging speed, and a wider field of view. In this review, we present the implementation and application of the state-of-the-art PACT systems using several types of curved US arrays: arc-shaped, ring-shaped, and hemispherical array transducers. Furthermore, we discuss the current limitations of PACT and also potential future directions for enhancing them.