  We study various aspects of the Carroll limit in which the speed of light is
sent to zero. A large part of this paper is devoted to the quantization of
Carroll field theories. We show that these exhibit infinite degeneracies in the
spectrum and may suffer from non-normalizable ground states. As a consequence,
partition functions of Carroll systems are ill-defined and do not lead to
sensible thermodynamics. These seemingly pathological properties might actually
be a virtue in the context of flat space holography.
  Better defined is the Carroll $\textit{regime}$, in which we consider the
leading order term in an expansion around vanishing speed of light without
taking the strict Carroll limit. Such an expansion may lead to sensible notions
of Carroll thermodynamics. An interesting example is a gas of massless
particles with an imaginary chemical potential conjugate to the momentum. In
the Carroll regime we show that the partition function of such a gas leads to
an equation of state with $w=-1$.
  As a separate story, we study aspects of Carroll gravity and couplings to
Carrollian energy-momentum tensors. We discuss many examples of solutions to
Carroll gravity, including wormholes, Maxwell fields, solutions with a
cosmological constant, and discuss the structure of geodesics in a Carroll
geometry. The coupling of matter to Carroll gravity also allows us to derive
energy-momentum tensors for hypothetical Carroll fluids from expanding
relativistic fluids as well as directly from hydrostatic partition functions.
