We present a detailed study of the electronic structure of the layered semiconductor InSe. We calculate the band structure of the monolayer and bulk material using density functional theory, hybrid functionals, and GW. The band gap of the monolayer InSe is calculated to be 2.4 eV in screened exchange hybrid functional, close to the experimental photoluminescence gap. The electron affinities and band offsets are calculated for vertical stacked-layer heterostructures, and are found to be suitable for tunnel field effect transistors (TFETs) in combination with WSe2 or similar. The valence-band edge of InSe is calculated to lie 5.2 eV below the vacuum level, similar to that for the closed shell systems HfSe2 or SnSe2. Hence InSe would be suitable to act as a p-type drain in the TFET. The intrinsic defects are calculated. For Se-rich layers, the Se adatom (interstitial) is found to be the most stable defect, whereas for In-rich layers, the Se vacancy is the most stable for the neutral state. Antisites tend to have energies just above those of vacancies. The Se antisite distorts towards a bond-breaking distortion as in the EL2 center of GaAs. Both substitutional donors and acceptors are calculated to be shallow, and effective dopants. They do not reconstruct to form nondoping configurations as occurs in black phosphorus. Finally, the Schottky barriers of metals on InSe are found to be strongly pinned by metal induced gap states (MIGS) at ∼0.5eV above the valence-band edge. Any interfacial defects would lead to a stronger pinning at a similar energy. Overall, InSe is an effective semiconductor combining the good features of 2D (lack of dangling bonds, etc.) with the good features of 3D (effective doping), which few others achieve.