  The study of crossing probabilities - i.e. probabilities of existence of
paths crossing rectangles - has been at the heart of the theory of
two-dimensional percolation since its beginning. They may be used to prove a
number of results on the model, including speed of mixing, tails of decay of
the connectivity probabilities, scaling relations, etc. In this article, we
develop a renormalization scheme for crossing probabilities in the
two-dimensional random-cluster model. The outcome of the process is a precise
description of an alternative between four behaviors:
  - Subcritical: Crossing probabilities, even with favorable boundary
conditions, converge exponentially fast to 0.
  - Supercritical: Crossing probabilities, even with unfavorable boundary
conditions, converge exponentially fast to 1.
  - Critical discontinuous: Crossing probabilities converge to 0 exponentially
fast with unfavorable boundary conditions and to 1 with favorable boundary
conditions.
  - Critical continuous: Crossing probabilities remain bounded away from 0 and
1 uniformly in the boundary conditions.
  The approach does not rely on self-duality, enabling it to apply in a much
larger generality, including the random-cluster model on arbitrary graphs with
sufficient symmetry, but also other models like certain random height models.
