  We discuss the relation between the cluster integrable systems and
$q$-difference Painlev\'e equations. The Newton polygons corresponding to these
integrable systems are all 16 convex polygons with a single interior point. The
Painlev\'e dynamics is interpreted as deautonomization of the discrete flows,
generated by a sequence of the cluster quiver mutations, supplemented by
permutations of quiver vertices.
  We also define quantum $q$-Painlev\'e systems by quantization of the
corresponding cluster variety. We present formal solution of these equations
for the case of pure gauge theory using $q$-deformed conformal blocks or
5-dimensional Nekrasov functions. We propose, that quantum cluster structure of
the Painlev\'e system provides generalization of the isomonodromy/CFT
correspondence for arbitrary central charge.
