Two-dimensional (2D) materials, in particular graphene and transition metal dichalcogenides (TMDC), have attracted great scientific interest over the last decade, revealing exceptional mechanical, electrical and optical properties. Owing to their layered nature, subnanometer-thick single-layer forms of these crystals can be chemically grown or mechanically isolated, representing an ultimately scaled-down platform for further miniaturization of electronic devices. Indeed, the large family of 2D materials contains hundreds of members, including metals, semiconductors, insulators, and others, covering the whole spectrum of potential applications. Availability of all necessary building blocks for the construction of all-2D solid-state devices makes this platform ideal for fabrication of ultrathin, transparent and flexible devices. Extensively investigated graphene has demonstrated excellent electrical properties. However, the absence of a bandgap is an obstacle for its interaction with light and therefore limits applications in optics. In this aspect, atomically thin TMDC semiconductors appear to be an alternative, more promising platform, as they possess a direct band gap in the visible range in the monolayer form. Despite being only three atoms thick, these semiconductors demonstrate exceptionally large light absorption, efficient light emission, and strong light-matter interaction, attracting justified interest from the optics community. We will focus on their potential applications for optoelectronics in Chapter 4. Even more, broken inversion symmetry and strong spin-orbit coupling in single-layer TMDC crystals reveal a new quantum number, the so-called valley index. Indeed, this unique degree of freedom of charge carriers is known for some materials since the 1970s. However, in the case of 2D semiconductors, spin-valley locking mechanism and valley contrasting optical selection rules open new ways for addressing, manipulation and sensing of this pseudospin, opening the whole new field of valleytronics. Due to the large splitting of the valence band, spin and valley degree of freedom become locked in these atomically thin materials. We employ this unique feature in Chapter 5 for indirect injection of spins into graphene by pumping valley polarized carriers in an adjacent TMDC monolayer. Being gapless, graphene does not allow direct optical injection of spins. Another striking feature of 2D materials is their unique ability to be stacked in vertical heterostructures with strong electrical coupling between layers. The weak van der Waals force, which keeps components together, provides freedom in the assembly process, so that a lattice mismatch or a twist angle becomes unimportant in the first approximation. This provides a novel platform for harvesting complementary properties of the constituent materials, allowing the engineering of new artificial meta-materials as we demonstrate in Chapter 6. Furthermore, synergistic effects in van der Waals heterostructures enable completely new properties and phenomena, which do not exist in the single materials, with twist angle being an important knob for tuning these effects. We observe and exploit such novel phenomena arising in heterostructures of 2D semiconductors in the last chapter of this thesis. On the way to the realization of practical optoelectronic and valleytronic applications, this thesis studies fundamental aspects of rich spin-valley physics of atomically thin semiconductors