  I discuss two related nonlinear mechanisms of tidal dissipation that require
finite tidal deformations for their operation: the elliptical instability and
the precessional instability. Both are likely to be important for the tidal
evolution of short-period extrasolar planets. The elliptical instability is a
fluid instability of elliptical streamlines, such as in tidally deformed
non-synchronously rotating or non-circularly orbiting planets. I summarise the
results of local and global simulations that indicate this mechanism to be
important for tidal spin synchronisation, planetary spin-orbit alignment and
orbital circularisation for the shortest period hot Jupiters. The precessional
instability is a fluid instability that occurs in planets undergoing axial
precession, such as those with spin-orbit misalignments (non-zero obliquities).
I summarise the outcome of local MHD simulations designed to study the
turbulent damping of axial precession, which suggest this mechanism to be
important in driving tidal evolution of the spin-orbit angle for hot Jupiters.
Avenues for future work are also discussed.
