Modern solid-state devices were made possible by the discovery of semiconductor heterostructures. Heterostructures offer the ability to fabricate low-dimensional nanostructures such as quantum dots which can restrain carriers in all three-directions. Quantum dots as single photon sources can be used as building blocks in quantum photonics and information processing applications. In this thesis, we explore heterostructures in nanowires and 2-D materials towards fabrication of quantum dots. In the first part, we show how facet-driven nanostructure self-assembly can be used to grow axial and radial QDs in lattice-mismatched NW heterostructures. We investigate the growth of InAs/GaAs nanowire heterostructure arrays on Si substrates using the Ga-catalyzed method. We show how the nanowire tip morphology affects the formation of axial In(Ga)As clusters. The occurrence of In-rich clusters on the nanowires is elucidated by electron microscopy. We also show how the In(Ga)As cluster formation on the nanowire sidewalls is driven by the convex nature of the {11-2} corner facets. Cathodoluminescence and photoluminescence maps close to the NW tip evidence the presence of optically active emission centers along the NW sidewalls. The second part is dedicated to heterostructures using monolayer 2-D transition-metal dichalcogenides. Firstly, we study the heterojunction between monolayer MoS2 and gold. We provide a detailed understanding of the microscopic origins behind Raman mode splitting in monolayer MoS2 exfoliated on gold substrates. We show that splitting in the Raman modes is a convolution of two effects: structural perturbations in MoS2 due to the Au-S interaction and breaking of symmetry rules by the metallic plasmons. We confirm the proposed hypothesis by using Al as the metal which does not show any peak splitting. In the last part, we successfully combine monolayer MoS2 with a GaAs NW array as a first step towards integrating monolayer 2-D materials with III-V nanowire arrays. Using detailed structural investigation, we show three different configurations of the MoS2 monolayer on NWs. Through confocal Raman and photoluminescence mapping, we show variations in the properties of the monolayer due to nanowires. We show how the vibrational properties are mainly affected by strain and charge transfer due to the nanowires. A blueshift in the luminescence attributing to an enhanced dielectric screening due to GaAs nanowires is observed. We show how III-V nanowires can be used to engineer the properties and enhance light extraction from monolayer 2-D materials.