Abstract: We discuss block-weighted map models in which random planar maps, possibly decorated by a statistical system, are canonically decomposed into elementary blocks, connected to each other by pinch points to form a tree structure. When a weight $u$ is assigned to each block, a phase transition occurs at a critical value, above which the maps degenerate into Brownian trees. The enumerative properties and critical exponents of maps below and at the critical value are linked by duality relations that are precisely those predicted by Liouville quantum gravity (LQG) when the dual measure is atomic. The Hausdorff dimensions of these objects also obey duality relations. At the dual critical point, we give the conditional distribution of the root block size given the total size, and conversely, the distribution of the total size for a fixed root block size, which perfectly agree with the results of LQG duality.  The ratio of dual and direct partition functions with punctures is shown to be universal, its explicit LQG expression exactly matching its combinatorial analogue. The block distance profile for doubly rooted maps is shown to be rigorously related to the distance profile of maps consisting of a single block. Finally, we consider the multifractal properties of the usual and dual Liouville measures. We illustrate these results through specific realizations of block-weighted maps, quadrangulations, the original Das et al. baby-universe model, and bicubic maps. For each model, we give the single non-universal constant which uniquely determines the strength of the corresponding atomic Liouville measure. Based on joint works with Emmanuel Guitter:   “Liouville Quantum Duality and Random Planar Maps I & II”, arXiv:2507.12203, arXiv:2604.24180.