CONSPECTUS: Nanostructures based on molybdenum disulfide (MoS2) are by far the most common and well-studied systems among two-dimensional (2D) semiconducting materials. Although still being characterized as a "promising material", catalytic activity of MoS2 nanostructures has been found, and applications in lubrication processes are pursued. Because exfoliation techniques have improved over the past years, monolayer MoS2 is easily at hand; thus, experimental studies on its electronic properties and applicability are in scientific focus, and some MoS2-based electronic devices have been reported already. Additionally, the improvement of atomic force microscopy led to nanoindentation experiments, in which the exceptional mechanical properties of MoS2 could be confirmed. In this Account, we review recent results from density-functional based calculations on several MoS2-based nanostructures; we have chosen to follow several experimental routes focusing on different nanostructures and their specific properties. MoS2-based triangular nanoflakes are systems that are experimentally well described and studied with a special focus on their optical absorption. The interpretation of our calculations fits well to the experimental picture: the absorption peaks in the visible light range show a quantum-confinement effect; they originate from excitations into the edge states. Additionally, delocalized metallic-like states are present close to the Fermi level, which do not contribute to photoabsorption in the visible range. Additionally, nanoindentation experiments have been simulated to obtain mechanical properties of the MoS2 material and to study the influence of deformation on the system's electronics. In these molecular-dynamics simulations, a tip penetrates a MoS2 monolayer, and the obtained Young's modulus and breaking stress agree very well with experimentally obtained values. Whereas the structural properties, such as bond lengths and layer contraction, vary locally differently upon indentation, the electronic structure in terms of the density of states, the gap between occupied and unoccupied states, or the quantum transport change only slightly. The robustness of the material with respect to electronic and mechanical properties makes monolayer MoS2 special. However, it is important to note that this robustness refers to a local disturbance through deformation and still seems to be dependent on the defect concentration. Finally, we present a comparison of the thermodynamic stabilities of different MoS2-based nanostructures with a focus on nanoflakes, fullerene-like nanooctahedra, and smaller Chevrel-type and non-Chevrel-type clusters (nanowires). All studied systems are stable in comparison to MoS2, Mo bulk, and the S8 crown, but only the studied nanoflakes and nanowires show specific stoichiometries, either sulfur-rich or sulfur-poor, whereas the nanooctahedra may adopt both. From the thermodynamic stabilities, it should be possible to deliberately choose specific nanostructures by thoughtful choices of the synthesis conditions. In conclusion, we present in this Account exceptional properties of MoS2-based nanostructures studied by means of density-functional theory. The focus lies on optical absorption in the visible range observed in triangular nanoflakes, which originate in the system's edge states, the robustness of monolayer MoS2 with respect to punctual loads regarding both mechanical and electronic properties, and the thermodynamic stability of most studied MoS2-based nanosystems revealing a correlation between composition and preferred morphology, particularly for 2D systems.