Random maps, which are simply random gluings of Euclidean polygons, provide natural models of discrete random surfaces that are expected to converge to universal continuum models of 2-dimensional random geometry, given in particular by Liouville quantum gravity surfaces. This is particularly well-understood in the context of "Brownian geometry" —a.k.a. LQG(\sqrt{8/3}) surfaces— which corresponds to limits of random maps with tame face degrees and in which the gluing is uniformly chosen among all possibilities. In this talk, we will study the situation where the gluing is still uniformly random, but where the faces are allowed to obey power-law degree distributions, leading in the scaling limit to random Sierpinski carpet or gasket-like objects. In the spirit of Pitman's "combinatorial stochastic processes", we will give a description of these limiting spaces in terms of classical objects of probability theory, namely, Lévy processes and Poisson random measures, and discuss its relationship with conformal loop ensembles. This is based on joint work with Nicolas Curien and Armand Riera.