Tunable nanophotonic metastructures offer new capabilities in computing, networking, and imaging by providing reconfigurability in computer interconnect topologies, new optical information processing capabilities, optical network switching, and image processing. Depending on the materials and the nanostructures employed in the nanophotonic metastructure devices, various tuning mechanisms can be employed. They include thermo-optical, electro-optical (e.g. Pockels and Kerr effects), magneto-optical, ionic-optical, piezo-optical, mechano-optical (deformation in MEMS or NEMS), and phase-change mechanisms. Such mechanisms can alter the real and/or imaginary parts of the optical susceptibility tensors, leading to tuning of the optical characteristics. In particular, tunable nanophotonic metastructures with relatively large tuning strengths (e.g. large changes in the refractive index) can lead to particularly useful device applications. This paper reviews various tunable nanophotonic metastructures' tuning mechanisms, tuning characteristics, tuning speeds, and non-volatility. Among the reviewed tunable nanophotonic metastructures, some of the phase-change-mechanisms offer relatively large index change magnitude while offering non-volatility. In particular, Ge-Sb-Se-Te (GSST) and vanadium dioxide (VO2) materials are popular for this reason. Mechanically tunable nanophotonic metastructures offer relatively small changes in the optical losses while offering large index changes. Electro-optically tunable nanophotonic metastructures offer relatively fast tuning speeds while achieving relatively small index changes. Thermo-optically tunable nanophotonic metastructures offer nearly zero changes in optical losses while realizing modest changes in optical index at the expense of relatively large power consumption. Magneto-optically tunable nanophotonic metastructures offer non-reciprocal optical index changes that can be induced by changing the magnetic field strengths or directions. Tunable nanophotonic metastructures can find a very wide range of applications including imaging, computing, communications, and sensing. Practical commercial deployments of these technologies will require scalable, repeatable, and high-yield manufacturing. Most of these technology demonstrations required specialized nanofabrication tools such as e-beam lithography on relatively small fractional areas of semiconductor wafers, however, with advanced CMOS fabrication and heterogeneous integration techniques deployed for photonics, scalable and practical wafer-scale fabrication of tunable nanophotonic metastructures should be on the horizon, driven by strong interests from multiple application areas.