Atomically thin films of III–VI post-transition metal chalcogenides (InSe and GaSe) form an interesting class of two-dimensional semiconductors that feature a strong variation of their band gap as a function of the number of layers in the crystal and, specifically for InSe, an expected crossover from a direct gap in the bulk to a weakly indirect band gap in monolayers and bilayers. Here, we apply angle-resolved photoemission spectroscopy with submicrometer spatial resolution (μARPES) to visualize the layer-dependent valence band structure of mechanically exfoliated crystals of InSe. We show that for one-layer and two-layer InSe the valence band maxima are away from the Γ-point, forming an indirect gap, with the conduction band edge known to be at the Γ-point. In contrast, for six or more layers the band gap becomes direct, in good agreement with theoretical predictions. The high-quality monolayer and bilayer samples enable us to resolve, in the photoluminescence spectra, the band-edge exciton (A) from the exciton (B) involving holes in a pair of deeper valence bands, degenerate at Γ, with a splitting that agrees with both μARPES data and the results of DFT modeling. Due to the difference in symmetry between these two valence bands, light emitted by the A-exciton should be predominantly polarized perpendicular to the plane of the two-dimensional crystal, which we have verified for few-layer InSe crystals.