Observations of exoplanet atmospheres have flourished in recent years, revealing a remarkable diversity of thermal, chemical and dynamical conditions. In particular, thermal emission observations of such atmospheres provide unique insights into their temperature profiles, chemistry and energy transport mechanisms. In this thesis, I explore the radiative and thermal conditions in exoplanets across a wide range of masses and irradiation conditions, from isolated brown dwarfs to rocky exoplanets. I begin by investigating important considerations for the atmospheric retrieval of isolated brown dwarfs. These objects provide remarkable laboratories for understanding atmospheric physics in the low-irradiation regime, and can be observed more precisely than exoplanets. As such, they provide a glimpse into the future of high-SNR observations of exoplanets. I introduce novel retrieval methods for isolated brown dwarfs, including a new temperature profile parameterisation and a method for including model uncertainty. I demonstrate this retrieval framework on both simulated and real data, showing that excellent precisions can be achieved on the inferred chemical abundances. I further investigate the temperature profiles and thermal emission spectra of hot Jupiters, including thermal inversions in their dayside atmospheres. In particular, TiO has long been proposed to cause thermal inversions in hot Jupiters and its spectral features in the optical and near-infrared have been detected. I investigate how TiO detections can depend on the molecular line list used to interpret the data, and how this sensitivity varies across different types of atmospheric observations. I also explore the occurrence of thermal inversions due to TiO and assess the performance of photometric metrics used to quantify them over a range in chemical composition, irradiation, gravity and stellar type. Recent optical observations of hot Jupiters in secondary eclipse are providing new constraints on their albedos and cloud/haze scattering. I investigate this for three hot Jupiters spanning a range of temperatures and gravities: KELT-1 b, WASP-18 b and WASP- 43 b. Using self-consistent atmospheric models, I interpret the optical to infrared spectra of these three targets and find that they can be explained by pure thermal emission, without the need for optical scattering by clouds or hazes. Furthermore, I find that inefficient day-night energy redistribution is needed to explain the high infrared fluxes from the daysides of these planets, consistent with previous works. I then explore the atmospheric conditions in mini-Neptunes, whose observations are beginning to provide constraints on their chemical and thermal properties, while also providing clues about their interiors and potential surfaces. With their relatively large scale heights and large planet-star contrasts, mini-Neptunes are currently ideal targets towards the goal of characterising temperate low-mass exoplanets. I explore the effects of irradiation, internal flux, metallicity, clouds and hazes on the atmospheric temperature profiles and thermal emission spectra of temperate mini-Neptunes. Building on recent suggestions of habitability of the mini-Neptune K2-18 b, I find a range of physically-motivated atmospheric conditions that allow for liquid water under the H2-rich atmospheres of such planets. I find that observations of thermal emission with the James Webb Space Telescope (JWST) can place useful constraints on the habitability of temperate mini-Neptunes such as K2-18 b. These results underpin the potential of temperate mini-Neptunes such as K2-18 b as promising candidates in the search for habitable exoplanets. Finally, I explore the characterisation of rocky exoplanet atmospheres across a wide temperature range. JWST will allow unprecedented characterisation of the atmospheres of small, rocky exoplanets. In particular, emission spectroscopy is an ideal technique to observe the secondary atmospheres of rocky exoplanets as such observations are not limited by the small scale height of high-mean-molecular-weight atmospheres. I develop a new retrieval framework tailored for rocky exoplanet atmospheres with unknown atmospheric constituents, and use this to assess the observability of promising, known rocky exoplanet targets. I find that the atmospheres of several known rocky exoplanets across a range of temperatures can be characterised using JWST.