Very little is known about giant planets and brown dwarfs at an orbital separation greater than 5~AU. And yet, these are important puzzle pieces needed for constraining the uncertainties that exist in giant planet formation and evolutionary models. The complex molecular chemistry of their atmospheres leaves a relatively wide parameter space for models to span. Placing accurate mass and luminosity data to observationally populate the mass-luminosity relationship provides a major contribution to an understanding of brown dwarf and giant planet evolutionary models. This thesis describes progress towards the detection, characterisation and monitoring of widely-separated giant planets and brown dwarfs through both direct imaging and long-period radial-velocities. This includes the detection of several long-period radial-velocity giant planets and brown dwarfs, as well as the direct imaging of some of these companions with VLT/SPHERE and the discovery of a benchmark $sim$50 $M_{mathrm{Jup}}$ T-type brown dwarf.