Beyond graphene there exist a rich family of two-dimensional crystals with a broad spectrum of electronic properties, which remain largely unexplored. For instance, a valley Hall semiconductor emerges by breaking the sublattice symmetry in the honeycomb structure. I will present our recent study of monolayer molybdenum disulfide as a protocol. The observation of an indirect-to-direct band gap crossover in the 2D limit and the optical orientation of its long-lived coupled valley-spins will be discussed. Furthermore, in some of the small-band-gap semiconductors with strong spin-orbit coupling, a new insulating phase with topologically protected surface states appears, due to inverted conduction and valence orbitals. I will show how surface-specific nonlinear optical probes are used to probe surface electrons in topological insulators.