We present the analysis of electronic band structure of InSe and (other III-VI semiconductors) films, from the stoichiometric mono-layer to N-layer films, and we describe the resulting optical properties of these 2D materials [1,2]. This study is based on the ab initio DFT and related multi-orbital tight-binding model analysis of the electronic band structure and wave functions in the two-dimensional N-layer InSe crystals, and it is compared to the results of luminescence spectroscopy of this material. We show [1-3] that the band gap in InSe (and GaSe) strongly depend on the number of layers, with a strong (more than twice) reduction from the monolayer to crystals with N>6. We find that the conduction-band- edge electron mass in few-layer InSe is quite light (comparable to Si), which suggests opportunities for high-mobility devices and the development of nanocircuits. In contrast, the valence band in mono-, bi- and trilayer InSe is flat, opening possibilities for strongly correlated hole gases in p-doped systems.  We also propose a model to describe electronic properties of misaligned layers of InSe. [1] D. Bandurin, A. Tyurnina, G. Yu, A. Mishchenko, V. Zólyomi, S. Morozov, R. Kumar, R. Gorbachev, Z. Kudrynskyi, S. Pezzini, Z. Kovalyuk, U. Zeitler, K. Novoselov, A. Patanè, L. Eaves, I. Grigorieva, V. Fal'ko, A. Geim, Y. Cao, Nature Nanotechnology (2016); doi:10.1038/nnano.2016.242 [2] Magorrian, S., Zolyomi, V. & Falko V. , Phys. Rev. B 94, 245431 (2016) [3] Mudd, G. W., Molas, M. R., Chen, X., Zólyomi, V., Nogajewski, K., Kudrynskyi, Z. R., Kovalyuk, Z. D., Yusa, G., Makarovsky, O., Potemski, M., Fal'ko, V. & Patanè, A., Scientific Reports. 6, 39619 (2016)