  We investigate the survival of planetesimal discs over Gyr timescales, using
a unified approach that is applicable to all Keplerian discs of solid bodies --
dust grains, asteroids, planets, etc. Planetesimal discs can be characterized
locally by four parameters: surface density, semi-major axis, planetesimal size
and planetesimal radial velocity dispersion. Any planetesimal disc must have
survived all dynamical processes, including gravitational instability,
dynamical chaos, gravitational scattering, physical collisions, and radiation
forces, that would lead to significant evolution over its lifetime. These
processes lead to a rich set of constraints that strongly restrict the possible
properties of long-lived discs. Within this framework, we also discuss the
detection of planetesimal discs using radial velocity measurements, transits,
microlensing, and the infrared emission from the planetesimals themselves or
from dust generated by planetesimal collisions.
