In this dissertation I have argued that the study of stars and gaseous planets has relied too heavily on simplifying assumptions. In particular, I have demonstrated that the assumptions of spherical symmetry, thermal equilibrium, dynamical equilibrium and turbulent anisotropy all hide interesting phenomena which make a true difference to the structure and evolution of these bodies. To begin I developed new theoretical tools for probing these phenomena, starting with a new model of turbulent motion which accounts for many different sources of anisotropy. Building on this I studied rotating convection zones and determined scaling relations for the magnitude of differential rotation. In slowly-rotating systems the differential rotation is characterised by a power law with exponent of order unity, while in rapidly-rotating systems this exponent is strongly suppressed by the rotation. This provides a full characterisation of the magnitude of differential rotation in gaseous convection zones, and is in reasonable agreement with a wide array of simulations and observations. I then focused on the convection zones of rotating massive stars and found them to exhibit significantly anisotropic heat fluxes. This results in significant deviations from spherical symmetry and ultimately in qualitatively enhanced circulation currents in their envelopes. Accordingly, these stars ought to live much longer and have a different surface temperature. This potentially resolves several outstanding questions such as the anomalously slow evolution of stars on the giant branch, the dispersion in the observed properties of giant stars and the difficulty stellar modelling has to form massive binary black holes. In the same vein I examined the convection zones of bloated hot Jupiters and discovered a novel feedback mechanism between non-equilibrium tidal dissipation and the thermal structure of their upper envelopes. This mechanism stabilises shallow radiative zones against the convective instability, which would otherwise take over early on in the planet's formation as it proceeds to thermal equilibrium. Hence tidal dissipation is dramatically enhanced, which serves to inject significant quantities of heat into the upper layers of the planet and causes it to inflate. This mechanism can explain most of the observed population of inflated planets. Finally, I studied material mixing in the outer layers of accreting stars and developed a method for relating the observed surface chemistry to the bulk and accreting chemistries. This enables the direct inference of properties of circumstellar material and accretion rates for a wide variety of systems.

Recent observations at the James Clerk Maxwell Telescope (JCMT) and elsewhere have identified a class of very deeply embedded, possibly protostellar, sources which are not associated with any of the traditional indicators of star formation, such as HII regions and near-infrared emission, but which do lie close to otherwise isolated H2O masers. This thesis describes a search, based on catalogues of known water maser positions, for new deeply embedded cores similar to those found in S106 and M17. In addition to millimetre molecular line and submillimetre continuum observations, 22 GHz and 8 GHz radio observations have been made of a number of the sources in order to obtain more accurate maser positions and to search for any associated compact HII regions. Observing sources such as these in less active star forming regions provides a cleaner environment in which to examine the maser excitation and the ongoing process of star formation. A sample of 44 water maser sources was observed from which submillimetre continuum emission was detected from 40 (91 per cent). The most striking feature of the data is the close association of the masers with the submillimetre cores: the data are consistent with masers occurring within 6000 AU of the embedded core. The results can be summarised as follows: o High temperature gas has been detected, and most of the submillimetre cores have mean densities greater than 10^6 /cm^3. o The masers have low velocities with respect to the molecular cloud and are uniformly distributed within 6600 AU of the submillimetre core. o The isotropic maser luminosity is proportional to the far-infrared luminosity over more than 5 orders of magnitude. o There is no obvious correlation between the near-infrared spectral class and the maser emission. o Where a radio spectral index is known the majority of sources are optically thin HII regions. The bulk of the remainder are undetected and have a flux density less than 1 mJy. o Masers not associated directly with a submillimetre core show explicit evidence for shocks. Embedded cores \emph{have} been detected with this survey and the maser emission is consistent with collisionally excited pump models.