There is broad agreement that the stars which explode as Type Ia supernovae are white dwarfs. They have accreted material in a binary system until they are near the Chandrasekhar mass and detonate/deflagrate. The two main scenarios for this accretion process are merging with a companion white dwarf (double degenerate scenario), or accretion from a main-sequence to red giant donor (single degenerate scenario). The donor star survives post-explosion and would provide substantial evidence for the single degenerate scenario, if found. Our team is analyzing stars in close proximity to Galactic Type Ia remnants to find surviving donor stars. In my talk I will introduce the different progenitor systems and the expected state for a donor star today. I will outline our search using high resolution spectroscopy and will present updated results.