Ferroelectric oxides are attractive materials for constructing efficient solar cells. The mechanism includes the anomalous photovoltaic effect (APE) and the bulk photovoltaic effect (BPE). The BPE refers to the generation of a steady photocurrent and above-bandgap photovoltage in a single-phase homogeneous material lacking inversion symmetry. The mechanism of BPE is different from the typical p-n junction-based photovoltaic mechanism in heterogeneous materials. We survey the history, development and recent progress in understanding the mechanisms of BPE, with a focus on the shift current mechanism, an intrinsic BPE that is universal to all materials lacking inversion symmetry. We also review the important factors to the APE, i.e., the domain boundary, the Schottcky junction, and the depolarization field. The recent successful applications of inorganic and hybrid perovskite structured materials in solar cells emphasize that ferroelectrics can be used in conventional photovoltaic architectures. We review the development in this field, with a particular emphasis on the perovskite materials and the theoretical explanations. In addition to discussing the implication of a ferroelectric absorber layer and the solid state theory of polarization, the design principles and prospect for high-efficiency ferroelectric photovoltaics are also mentioned. Considering the coupling between the degrees of freedom, some special ferroelectrics are expected to have prominent multi-functionality. With the introduction of the additional degree of freedom, some ferroelectrics, i.e., ScFexCr1-xO3 (1/6 x 5/6), can be a promising candidate for highly efficient solar cells and spin photovoltaic devices.