Metasurfaces can be opportunely and specifically designed to manipulate electromagnetic wavefronts. In recent years, a large variety of metasurface-based optical devices such as planar lenses, beam deflectors, polarization converters, and so on have been designed and fabricated. Of particular interest are tunable metasurfaces, which allow the modulation of the optical response of a metasurface; for instance, the variation in the focal length of a converging metalens. Response tunability can be achieved through external sources that modify the permittivity of the materials constituting the nanoatoms, the substrate, or both. The modulation sources can be classified into electromagnetic fields, thermal sources, mechanical stressors, and electrical bias. Beside this, we will consider optical modulation and multiple approach tuning strategies. A great variety of tunable materials have been used in metasurface engineering, such as transparent conductive oxides, ferroelectrics, phase change materials, liquid crystals, and semiconductors. The possibility of tuning the optical properties of these metamaterials is very important for several applications spanning from basic optics to applied optics for communications, depth sensing, holographic displays, and biochemical sensors. In this review, we summarize the recent progress on electro-optical magnetic, mechanical, and thermal tuning of metasurfaces actually fabricated and experimentally tested in recent years. At the end of the review, a short section on possible future perspectives and applications is included.