Several giant planets have now been directly imaged, offering the first view of extrasolar planets at wide separations from their host stars. Formation of these objects, either by core accretion or gravitational instability, presents substantial theoretical difficulties. In this talk, I will discuss the challenges and opportunities posed by wide-separation planets for theories of planet formation and orbital evolution. I will emphasize (1) a new theory of planetary core growth in the presence of gas that extends the reach of core accretion to large stellocentric distances and (2) new constraints on the dynamical history of the outer solar system.