  Rayleigh-B\'enard convection in rotating spherical shells can be considered
as a simplified analogue of many astrophysical and geophysical fluid flows.
Here, we use three-dimensional direct numerical simulations to study this
physical process. We construct a dataset of more than 200 numerical models that
cover a broad parameter range with Ekman numbers spanning $3\times 10^{-7} \leq
E \leq 10^{-1}$, Rayleigh numbers within the range $10^3 < Ra < 2\times
10^{10}$ and a Prandtl number unity. We investigate the scaling behaviours of
both local (length scales, boundary layers) and global (Nusselt and Reynolds
numbers) properties across various physical regimes from onset of rotating
convection to weakly-rotating convection. Close to critical, the convective
flow is dominated by a triple force balance between viscosity, Coriolis force
and buoyancy. For larger supercriticalities, a subset of our numerical data
approaches the asymptotic diffusivity-free scaling of rotating convection
$Nu\sim Ra^{3/2}E^{2}$ in a narrow fraction of the parameter space delimited by
$6\,Ra_c \leq Ra \leq 0.4\,E^{-8/5}$. Using a decomposition of the viscous
dissipation rate into bulk and boundary layer contributions, we establish a
theoretical scaling of the flow velocity that accurately describes the
numerical data. In rapidly-rotating turbulent convection, the fluid bulk is
controlled by a triple force balance between Coriolis, inertia and buoyancy,
while the remaining fraction of the dissipation can be attributed to the
viscous friction in the Ekman layers. Beyond $Ra \simeq E^{-8/5}$, the
rotational constraint on the convective flow is gradually lost and the flow
properties vary to match the regime changes between rotation-dominated and
non-rotating convection. The quantity $Ra E^{12/7}$ provides an accurate
transition parameter to separate rotating and non-rotating convection.
