Recent discoveries of several transiting planetswith clearly non-zero eccentricities and some large obliquities started changing the simple picture of close-in planets having circular and well-aligned orbits. The two major scenarios that form such close-in 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. Most of these close-in planets experience orbital decay all the way to the Roche limit as previous studies showed.We investigate the tidal evolution of transiting planets on eccentric orbits, and find that there are two characteristic evolution paths for them, depending on the relative efficiency of tidal dissipation inside the star and the planet. Our study shows that each of these paths may correspond to migration and scattering scenarios. We further point out that the current observations may be consistent with the scattering scenario, where the circularization of an initially eccentric orbit occurs before the orbital decay primarily due to tidal dissipation in the planet, while the alignment of the stellar spin and orbit normal occurs on a similar timescale to the orbital decay largely due to dissipation in the star.We also find that even when the stellar spin-orbit misalignment is observed to be small at present, some systems could have had a highlymisaligned orbit in the past, if their evolution is dominated by tidal dissipation in the star. Finally, we also re-examine the recent claim by Levrard et al. that all orbital and spin parameters, including eccentricity and stellar obliquity, evolve on a similar timescale to orbital decay. This counterintuitive result turns out to have been caused by a typo in their numerical code. Solving the correct set of tidal equations, we find that the eccentricity behaves as expected, with orbits usually circularizing rapidly compared to the orbital decay rate.