Current observational estimates suggest that similar to 30% of all binary s
tars are in triple systems. In similar to 70% of these, the enclosed binary
is close enough that the primary in the binary can evolve to fill its Roch
e lobe. In similar to 10%-20%, the third, more distant component can evolve
to fill its Roche lobe, leading to configurations inaccessible to isolated
binary stars. Triple stars are unstable if the ratio of the orbital period
of the enclosed binary to the period of the third component exceeds a crit
ical value. Hence, an increase in the orbital period of the binary due to c
onservative mass transfer between components or to wind mass loss from the
binary can destabilize an initially stable triple system, causing it to dec
ompose into a rapidly moving single star and an evolved binary recoiling in
the opposite direction with a velocity large compared with velocities typi
cal of primordial binaries. To highlight the different possibilities inhere
nt in triple-star evolution, we discuss qualitatively several possible scen
arios whereby triple stars with component masses in the range 1-10 M. can e
volve into Type Ia supernovae, which we assume to be explosions of merging
carbon-oxygen or oxygen-neon white dwarfs of total mass larger than 1.4 M..
Before quantitative predictions of the likelihood of these scenarios can b
e made, it is necessary to determine the initial distribution of young trip
le stars over their masses and orbital separations and to calculate the rea
ction of the enclosed binary to matter transferred to it by the third compo
nent when it fills its Roche lobe or supports a strong wind.