  This chapter concerns the long-term dynamical evolution of planetary systems
from both theoretical and observational perspectives. We begin by discussing
the planet-planet interactions that take place within our own Solar System. We
then describe such interactions in more tightly-packed planetary systems. As
planet-planet interactions build up, some systems become dynamically unstable,
leading to strong encounters and ultimately either ejections or collisions of
planets. After discussing the basic physical processes involved, we consider
how these interactions apply to extrasolar planetary systems and explore the
constraints provided by observed systems. The presence of a residual
planetesimal disc can lead to planetary migration and hence cause instabilities
induced by resonance crossing; however, such discs can also stabilise planetary
systems. The crowded birth environment of a planetary system can have a
significant impact: close encounters and binary companions can act to
destabilise systems, or sculpt their properties. In the case of binaries, the
Kozai mechanism can place planets on extremely eccentric orbits which may later
circularise to produce hot Jupiters.
