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Thermonuclear Supernovae (SNe Ia) are one of the building blocks of modern cosmology and laboratories for the explosion physics of White Dwarf star/s (WD) in close binary systems. The second star may be aWD(double degenerate systems, DD), or a non-degenerated star (SD) with a main sequence star, red giant or a helium star as companion (Branch et al. 1995; Nomoto et al. 2003; Wang & Han 2012). Light curves and spectra of the explosion look similar because a ’stellar amnesia’ (H¨oflich et al. 2006). Basic nuclear physics determines the progenitor structure and the explosion physics, breaking the link between progenitor evolution, and the explosion, resulting in three main classes of explosion scenarios: a) dynamical merging of two WD and a heating on time scales of seconds (Webbink 1984; Isern et al. 2011), b) surface helium detonations on top of a WD which ignite the central C/O by a detonation wave traveling inwards (Nomoto 1982; Hoeflich & Khokhlov 1996; Kromer et al. 2010); c) compressional heating in an accreting WD approaching the Chandrasekar mass on time of up to 108 years which may originated from SD and DD systems (Whelan & Iben 1973; Piersanti et al. 2003). Simulations of the explosions depend on the inital conditions at the onset of the explosions, namely the mass and angular momentum of the WD(s). For all scenarios, diversity in SNe Ia must be expected because the WD originates from a range of Main Sequence masses (MMS < 8M ) and metallicities Z. Moreover, there is growing evidence that magnetic fields B may have to be added to the ’mix’. Only with recent advances in observations ranging from X-ray to radio, high precision spectroscopy, polarimetry and photometry and in the time-domain astronomy we obtain constraints for progenitor, on the explosion scenarios and links emerge between the progenitors and their environment with LCs and spectral signatures needed for high precision cosmology. It is too early to give final answers but we present our personal view. We will give some examples from the theory point of view and discuss future prospects with upcoming ground based, ELT, GMT and space based such as JWST, Euclide and WFIRST instruments.