Supernovae (SNe) are the explosive deaths of stars, but the detailed properties of their progenitors are not well understood. For example, while we know Type Ia SNe are explosions of white dwarfs (WDs), it is unclear whether these WDs generally have a stellar companion or another WD companion. For core-collapse SNe, whose progenitors are stars >8 M⊙, it is unclear whether stars >18 M⊙ produce a visible SN, or directly collapse to a black hole in a weak transient event. For my dissertation, I have focused on using high-quality surveys of SN remnants, stellar populations and interstellar medium in our Local Group galaxies to understand the possible progenitor scenarios of SNe. The goal is to make an accurate measurement of the SN delay-time distribution (DTD), which is the rate of SNe versus stellar evolutionary timescale, assuming these stars were all formed in a burst. The DTD can constrain which set of progenitor models are consistent with the population of Type Ia and core-collapse SNe in a survey. To achieve this goal, I have constructed a model of a SN remnant survey in the Local Group that can estimate the visibility times of a SN remnants as a function of their environment. This can be combined with existing high-quality stellar age distribution maps, constructed from resolved stellar populations, to measure the most accurate DTD. I also calculated DTDs of pulsating variables like RR Lyrae and Cepheids, and found a distribution of evolutionary timescales which are not predicted by canonical models. This helped understand possible systematics in the DTD method, and also reassess the progenitor scenarios of astrophysically significant objects like RR Lyrae and Cepheids in the era of big data surveys. Finally, I used direct observations and modeling of radio emission of old SNe/young SN remnants such as SN 1885A and G1.9+0.3 as an alternative, but promising avenue for determining the possible progenitor scenarios of Type Ia SNe
