We will review the physical mechanisms involved in the dynamical evolution of Trans-Neptunian binaries (TNBs). They include: gravitational encounters with massive objects, the impulse transferred in the collisions with objects of the background population of Trans-Neptunian objects, Kozai oscillations of the binary mutual orbit induced by the Sun and planets, and tidal friction on both the primary and the secondary component of the binary and perturbations due to their nonsphericity. Then, we will show that, acting together, all these effects seem to explain most of the orbital characteristics of the known binary systems. Given the number of surviving binaries after 4.5 Gyr of dynamical evolution and the binary fraction observed today, it is plausible to suggest that all the planetesimals in the outer solar system should have been born as binaries or multiple systems. TNB belonging to the Centaur population have short dynamical lifetimes. In the frame of the present understanding of binary evolution in the outer solar system, binary Jupiter Family Comets would be found mainly in the form of contact binaries. If a population of binary systems survived to the instability phase of the outer solar system as Neptune Trojans, we would have at present a considerable fraction of them already in the Trojan Clouds. The observational evidence does not rule out this possibility. As the dynamical evolution of TNB involves strong diffusive mechanisms that could erase much of their primordial orbital structure, it would be necessary to accumulate more observational data and the computations of mutual orbits, to impose definitive constraints on the proposed formation mechanisms.