This paper intends a short review of the research work done on the structural and electronic properties of layered Indium Selenide (InSe) and related III-VI semiconductors under high pressure conditions. The paper will mainly focus on the crucial role played by high pressure experimental and theoretical tools to investigate the electronic structure of InSe. This objective involves a previous revision of results on the pressure dependence of the InSe crystal structure and related topics such as the equation of state and the pressure-temperature crystal phase diagram. The main part of the paper will be devoted to reviewing the literature on the optical properties of InSe under high pressure, especially the absorption experiments that led to the identification of the main optical transitions, and their assignment to specific features of the electronic structure, with the help of modern first-principles band structure calculations. In connection with these achievements we will also review relevant results on the lattice dynamical, dielectric, and transport properties of InSe, as they provided very useful supplementary information on the electronic structure of the material.