Thin film solar cells are one of the important candidates utilized to reduce the cost of photovoltaic production by minimizing the usage of active materials. However, low light absorption due to low absorption coefficient and/or insufficient active layer thickness can limit the performance of thin film solar cells. Increasing the absorption of light that can be converted into electrical current in thin film solar cells is crucial for enhancing the overall efficiency and in reducing the cost. Therefore, light trapping strategies play a significant role in achieving this goal. The main objectives of light trapping techniques are to decrease incident light reflection, increase the light absorption, and modify the optical response of the device for use in different applications. Nanostructures utilize key sets of approaches to achieve these objectives, including gradual refractive index matching, and coupling incident light into guided modes and localized plasmon resonances, as well as surface plasmon polariton modes. In this review, we discuss some of the recent developments in the design and implementation of nanostructures for light trapping in solar cells. These include the development of solar cells containing photonic and plasmonic nanostructures. The distinct benefits and challenges of these schemes are also explained and discussed.