We present observational and theoretical studies constraining Type Ia supernova progenitors. First, we use a new observational technique to show that "prompt" SNe Ia that trace star-formation on cosmic timescales exhibit a significant delay time of 200-500 million years. This implies that either the majority of SNe Ia companion stars have main-sequence masses less than three solar masses, or that most SNe Ia arise from double-white dwarf binaries. Second we present a comprehensive study of white dwarf collisions as an avenue for creating SNe Ia. Using a smooth particle hydrodynamics code with a 13-isotope nuclear network, we show that several combinations of white dwarf masses and impact parameters produce enough 56Ni to result in luminosities ranging from those of sub-luminous to super-luminous SNe Ia, depending on the parameters of the collision. Finally, we conduct a simulation survey of double-degenerate white dwarf mergers with varying mass combinations. Unlike previous works, we do not add detonations by hand to our simulations, and we do not find any thermonuclear explosions during the mergers. Instead, all but one of our simulations forms a cold, degenerate core surrounded by a hot disk, while our least massive pair of stars forms only a hot disk. We characterize the remnants by core mass, rotational velocity, and half-mass radius, and discuss how we will evolve them further with simulations that incorporate dissipative processes. Such simulations may indeed lead to double-degenerate Type Ia explosions that occur many orbits after the mergers themselves.