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Liouville quantum gravity (LQG) is a natural model for a randomÌýfractal surface with origin in the physics literature. A powerful tool inÌýthe study of LQG is conformal welding, where multiple LQG surfaces areÌýcombined into a single LQG surface. The interfaces between the original LQGÌýsurfaces are typically described by variants of the random fractal curvesÌýknown as Schramm-Loewner evolutions (SLE). We will present a few recentÌýconformal welding results for LQG surfaces and their applications, whichÌýrange from SLE and LQG to planar maps and random permutations. Based onÌýjoint works with Ang and Sun, with Lehmkuehler, and with Borga, Sun and Yu.