A quarter-millennium ago, Lagrange demonstrated the existence of five equilibrium positions in the three-body problem. Associated with these equilibria are so-called Trojan and horseshoe orbits, offering safe havens for small body populations near the orbits of planets and satellites (eg the Jupiter Trojans, co-orbiting moons in the Saturn system). The continuing effort to complete our inventory of the solar system led to the discovery, in the 1990s, of new types of coorbitals not predicted by contemporary theoretical models. New treatments of the coorbital resonance developed since then showed that the large eccentricities and inclinations typical of near-Earth asteroids and other bodies in heliocentric orbit give rise to new modes of libration in the 1:1 resonance. These new dynamics act as protection mechanisms against planetary collision and lead to stable orbit transitions due to the secular evolution of the orbit. In this presentation, I will demonstrate the key features of coorbital motion for arbitrary e and I orbits and show how these manifest in the real solar system, using Earth coorbital asteroids as examples.