The bulk photovoltaic effect is a second-order nonlinear photoelectric response, which refers to a phenomenon that non-centrosymmetric structural material generates a steady-state photocurrent under uniform light irradiation. The bulk photovoltaic effect has attracted widespread attention due to its open-circuit voltage is not limited by the semiconductor bandgap and power conversion efficiency breaks through the Shockley-Queisser limit. In addition, the bulk photovoltaic effect is closely related to the quantum geometric properties (such as Berry curvature and quantum metric) of solids, thus making it an effective means to study crystal polarization, orbital magnetization, and quantum Hall effects. Two-dimensional (2D) materials are rich in electrical, optical, magnetic, topological properties and their interactions, which can effectively improve the performances of bulk photovoltaic devices (such as expanding response range of bulk photovoltaic effect) and have important research value for exploring basic physical problems. This paper reviews the development process of bulk photovoltaic effect and its physical mechanism. The research progress of bulk photovoltaic effect in 2D materials is discussed in detail, including single component 2D materials, 2D material stacking engineering (such as 2D material homojunctions and heterojunctions), and other factors (such as magnetic field, strain engineering) to generate or regulate the bulk photovoltaic effect response. Finally, the development prospect of two-dimensional bulk photovoltaic effect is prospected.