Despite the critical role that Type Ia supernovae (SNe Ia) play in the chemical enrichment of the Universe and their great importance in measuring cosmological distances, we still don't know for certain how they arise. Most models can be broadly grouped into either "accretion" or "merger" scenarios, with the former typically implying a hot, luminous phase (0.1 -- 1 million K, 10^38 erg/s) at some point prior to explosion. Past efforts to directly detect the progenitors of very recent, nearby SNe Ia in archival soft X-ray images have produced only upper limits, and are only constraining assuming progenitors with very high temperatures immediately preceding the explosion. In this talk, I will outline our new approach: given that such objects should be strong sources of ionizing radiation, one may instead search the environment surrounding nearby SN Ia remnants for interstellar matter ionized by the progenitor. Such ''relic'' nebulae should extend out to tens of parsecs and linger for roughly the recombination timescale in the ISM, of order 10,000 -- 100,000 years. With this in mind, I will introduce our new narrow-band survey for relic nebulae surrounding young Magellanic SN Ia remnants and accreting white dwarfs, already underway using the Magellan Baade telescope (PI: Alejandro Clocchiatti). In a similar manner, we have also placed deep upper limits on the temperatures and luminosities of the progenitors of Tycho (SN 1572) and other Galactic SNe Ia from the study of their Balmer-dominated shocks. In addition to opening a new era of ''SN Ia archaeology'', I will also discuss how these results can put new constraints on binary population synthesis models.