Second-order (χ(2)) optical nonlinearity is one of the most common mechanisms for modulating and generating coherent light in photonic devices. Due to strong photon confinement and long photon lifetime, integrated microresonators have emerged as an ideal platform for investigation of nonlinear optical effects. However, existing silicon-based materials lack a χ(2) response due to their centrosymmetric structures. A variety of novel material platforms possessing χ(2) nonlinearity have been developed over the past two decades. This review comprehensively summarizes the progress of second-order nonlinear optical effects in integrated microresonators. First, the basic principles of χ(2) nonlinear effects are introduced. Afterward, we highlight the commonly used χ(2) nonlinear optical materials, including their material properties and respective functional devices. We also discuss the prospects and challenges of utilizing χ(2) nonlinearity in the field of integrated microcavity photonics.