  Recent discoveries of several transiting planets with clearly non-zero
eccentricities and some large inclinations started changing the simple picture
of close-in planets having circular and well-aligned orbits. Two major
scenarios to form such planets are planet migration in a disk, and
planet--planet interactions combined with tidal dissipation. The former
scenario can naturally produce a circular and low-obliquity orbit, while the
latter implicitly assumes an initially highly eccentric and possibly
high-obliquity orbit, which are then circularized and aligned via tidal
dissipation. We investigate the tidal evolution of transiting planets on
eccentric orbits. We show that the current and future orbital evolution of
these systems is likely dominated by tidal dissipation, and not by a more
distant companion. Although most of these close-in planets experience orbital
decay all the way to the Roche limit, there are two characteristic evolution
paths for them, depending on the relative efficiency of tidal dissipation
inside the star and the planet. We point out that the current observations may
be consistent with one of them. Our results suggest that at least some of the
close-in planets with non-zero orbital eccentricity may have been formed by
tidally circularizing an initially eccentric orbit. We also find that even when
the stellar spin-orbit misalignment is observed to be small at present, some
systems could have had a highly misaligned orbit in the past. Finally, we also
re-examine the recent claim by Levrard et. al., who found that all orbital and
spin parameters evolve on a similar timescale to orbital decay.
