  (${Abridged~version}$) We review how the single degenerate models for Type Ia
supernovae (SNe Ia) works. In the binary star system of a white dwarf (WD) and
its non-degenerate companion star, the WD accretes either H-rich matter or He
and undergoes H and He shell-burning. We summarize how such shell-burning
depend on the accretion rate and the WD mass and how the WD blows strong wind.
We identify the following evolutionary routes for the accreting WD to trigger a
thermonuclear explosion. With a decreasing rate with time, 5 phases are
observed: 1. The WD increases its mass by stable H burning and blows a strong
wind, which strips a part of the companion star's envelope to control the
accretion rate and forms circumstellar matter (CSM). The WD may explode within
CSM as an "SN Ia-CSM". 2. The wind stops and an SN Ia is triggered under
steady-stable H shell-burning, which is observed as a super-soft X-ray source:
"SN Ia-SSXS". 3. H shell-burning becomes unstable and many flashes recur. The
WD undergoes recurrent nova (RN) whose mass ejection is smaller than the
accreted matter, evolving to an "SN Ia-RN". 4. If the companion is a He star or
WD, the accretion of He can trigger He and C double detonations at the
sub-Chandrasekhar (sub-Chand) mass or the WD grows to the Chand mass while
producing and He-wind: "SN Ia-He CSM". 5. If the accreting WD rotates rapidly,
delayed trigger of an SN Ia beyond standard Chand mass can happen. The
(super-Chand) WD contracts to become a delayed SN Ia after losing angular
momentum. The companion star has become a He WD and CSM has disappeared: "SN
Ia-He WD". We update nucleosynthesis yields of the carbon deflagration model
W7, delayed detonation model WDD2, and the sub-Chand mass model to constrain
the yields (such as Mn) by comparing the observations. We note the important
metallicity effects on $^{58}$Ni and $^{55}$Mn.
