  We discuss the asymptotic behaviour of random critical Boltzmann planar maps
in which the degree of a typical face belongs to the domain of attraction of a
stable law with index $\alpha \in (1,2]$. We prove that when conditioning such
maps to have $n$ vertices, or $n$ edges, or $n$ faces, the vertex-set endowed
with the graph distance suitably rescaled converges in distribution towards the
celebrated Brownian map when $\alpha=2$, and, after extraction of a
subsequence, towards another `$\alpha$-stable map' when $\alpha <2$, which
improves on a first result due to Le Gall & Miermont who assumed slightly more
regularity.
