The planets of the Solar System possess cloud structures and weather systems with a great diversity of shapes, sizes, lifetimes, and brightnesses. As a planet rotates on its axis, these features rotate in and out of view and thereby induce changes in the total brightness of the planet as seen from afar. In this thesis, I develop new, bespoke techniques to look for similar brightness variability in the light curves of exoplanets and brown dwarfs, which can provide an insight into their weather, atmospheric structure, and visual appearance. Coronagraph-equipped ground-based observatories have the resolution and photon collecting power needed to monitor these faint, close-separation, companions, but lack access to the photometric references needed to correct for non-astrophysical variability introduced by turbulence in Earth’s atmosphere. Uniquely, the vector Apodizing Phase Plate (vAPP) coronagraph enables observations of faint companions while maintaining an image of the host star for use as a photometric reference to remove contaminant variability. Using observations obtained with vAPP coronagraphs, I characterise the atmospheres of substellar companions and search for variability in their light curves. By combining the vAPP with an integral field spectrograph to enable differential spectrophotometry, I adapt concepts from the field of exoplanet transmission spectroscopy. I show that with the new techniques that I have developed we can reach 4% precision levels, repeatable on separate nights, and I highlight that improvements in wavefront sensing and systematics detrending could provide even greater precision, which will ultimately bring the features of distant worlds into sharper view.