The monolayer semiconducting transition metal dichalcogenides are a family of 2D crystals that, beginning with MoS2 and soon expanding to include tungsten and other chalcogen variants, has become a focus of much research in 2D materials. Their semiconductor character, with wide direct bandgaps in the visible and near-infrared energy spectrum, make them particular amenable to optoelectronic applications. The low-dimensional character leads the direct gaps to host tightly bound exciton states that are stable at room temperature, allowing for the experiments on exciton physics that were only accessible at low temperatures in classical 2D excitonic system such as GaAs 2D quantum wells. The crystal structure of TMDs further gives the excitons and other quasi-particles valley contrasting physics, which can be discriminated optically with circularly polarized light, and leads to phenomena such as the valley Hall effect. The combination of strong light-matter interactions in TMDs with novel physics makes optical spectroscopy and microscopy powerful tools in the characterization of these materials. However, the native length scales of the excitons, while larger than the lattice constant, are still far below the resolution of optical probes. This resolution is set by the diffraction limit of light, which limits the focusing of propagating electromagnetic fields to roughly half the wavelength. Optical probes will effectively average over large areas (200 x 200 nm2) of the crystal, obscuring the effects of highly localized and heterogeneous perturbations. The need for local experimental probes in the study of TMDs has been highlighted by the recent discovery of single-photon emission from monolayer WSe2. Many far-field experimental works have shown a strong association of the emergence of these emitters and regions inhomogeneous tensile strain, leading to the hypothesis of quantum confinement of the excitons by the strain-created potential wells. However, experimental investigation of this hypothesis is challenging due to the scale mismatch of the localized excitons, which must be on order the exciton Bohr radius of ~ 1 nm, and the ~ 250 nm size of the optical probes. The focus of this work is to bridge the resolution gap of optical microscopy and spectroscopy in the study of excitons in the 2D TMDs using scanning near-field optical microscopy (SNOM), which allows optical resolutions down to a few nanometers. Using this technique to measure spectra of photoluminescence (PL) and scattering from lattice vibrations (Raman scattering), I investigate the nanoscale interplay of strain and the excitons in several of the commonly studied semiconducting TMDs, including WS2, WSe2, and MoSe2. In this thesis, I first discuss methods of performing near-field optical studies on 2D materials, including aperture and apertureless SNOM methods, and demonstrate them by collecting real nanoscale PL (nano-PL) and nano-Raman on WS2 and WSe2. Following that, I show how to estimate the strain in nanobubbles from classical models of plate bending, and show by comparison with shifts in the lattice vibrations that such models on average correctly estimate the strain. Further, by combining high-resolution nano-PL of WSe2 with advanced microscopic theories, I show evidence that strain alone can efficiently localized excitons at room temperature due to formation of atomic scale wrinkles of the crystal. Using gap-mode nano-PL with nanometer resolution, I demonstrate that the spatial location of localized exciton emission in WSe2 occurs along a common axis over several nanobubbles, and that it is highly localized in the wrinkle-like rings in asymmetric nanobubbles. Lastly, investigation of nanobubbles in MoSe2/WSe2 heterostructures shows that similar wrinkle-like ring structures occur commonly in large nanobubbles, and that such structures host strong exciton complexes in energetic regions associated with the interlayer exciton. This emission is unusually strong at room temperature, and has emission peaks that extend passed 1000 nm, which has not been previous described in such heterostructures. The results presented here show the strong and rich interplay of excitons with strain, demonstrating the utility of strain-engineering in future TMD devices, but also represent a frontier in studying the physics of confined excitons both spectrally and spatially.