The following dissertation focuses on a new class of devices based on singularities of non-Hermitian photonic systems for applications pertaining to sensing and lasing. These are systems with electromagnetic resonances that exhibit peculiar behavior. One in which multiple resonances of shared symmetry coalesce to form so called Exceptional Point (EP) singularities. Systems at EPs are known to be highly sensitive to environmental perturbations making them conducive for sensing applications. The first half of this dissertation is centered on investigating resonance dynamics of plasmonic nanostructures, comprised of metallic nano-particles, as they have the ability to confine light to an extremely small space (i.e. sub-wavelength) which in turn helps detect particles of equivalent size. Herein, a framework for designing EPs in coupled metallic nano-particle arrays is presented. The latter half is centered on another type of peculiarity in which a resonance lifetime in a cavity diverges to infinity (i.e. infinite quality factor). These are resonance states that defy conventional wisdom by remaining localized, or bound, to a cavity while residing in a continuum of radiating or leaky states. These singularities are appropriately termed Bound States in the Continuum (BICs). This dissertation presents the first experimental demonstration of a BIC laser. It is constructed on a III-V semiconductor material platform (InGaAsP) which emits in the telecommunication band (~1.55 μm) and operates at room temperature. This laser is intrinsically low threshold (i.e., power efficient) and can be compact in size. It offers some unique and useful properties in terms of its tunability in emission wavelength and emission angle. It has the ability to naturally generate vector beams and the potential for high-power emission. A brief discussion on challenges to real-world applications is provided for these technologies.