  The physical nature of fast radio bursts (FRBs) is not identified. Detecting
electromagnetic counterparts in other wavelengths is essential to measure their
distances and to settle down their physical nature. Assuming that at least some
of them are of a cosmological origin, we calculate their afterglow lightcurves
in multi-wavelengths (X-rays, optical and radio) by assuming a range of their
total kinetic energies and redshifts. We focus on forward shock emission, but
also consider the possibility that some of them might have bright reverse shock
emission. In general, the FRB afterglows are too faint to be detected by
current detectors. Only if an FRB has a very low radiative efficiency in radio
(hence, a very large kinetic energy), and when it is close enough, can its
afterglow be detected in the optical and radio bands. We discuss observational
strategies to detect these faint afterglows using future telescopes such as
LSST and EVLA.
