  Binary black holes with misaligned spins will generically induce both
precession and nutation of the orbital angular momentum $\bf{L}$ about the
total angular momentum $\bf{J}$. These phenomena modulate the phase and
amplitude of the gravitational waves emitted as the binary inspirals to merger.
We introduce a "taxonomy" of binary black-hole spin precession that encompasses
all the known phenomenology, then present five new phenomenological parameters
that describe generic precession and constitute potential building blocks for
future gravitational waveform models. These are the precession amplitude
$\langle\theta_L\rangle$, the precession frequency $\langle \Omega_L\rangle$,
the nutation amplitude $\Delta\theta_L$, the nutation frequency $\omega$, and
the precession-frequency variation $\Delta\Omega_L$. We investigate the
evolution of these five parameters during the inspiral and explore their
statistical properties for sources with isotropic spins. In particular, we find
that nutation of $\bf{L}$ is most prominent for binaries with high spins ($\chi
\gtrsim 0.5$) and moderate mass ratios ($q \sim 0.6$).
