Redistricting is the problem of partitioning a set of geographic units into a fixed number of subsets called districts, subject to a list of rules and priorities. These districts are used for elections, making their delineation highly consequential. It has been hard for quantitative researchers to orient to an application domain in which rule vagueness can be a feature rather than a bug-but law and policy often prefer a reasonable range of values to a paradigm of optimization. In recent years, the use of randomized methods to sample from the vast space of districting plans has been gaining traction in U.S. courts of law for identifying partisan gerrymanders, and it is now emerging as a promising assessment tool for legislatures and independent commissions, even before districts are enacted. In this article, we set up redistricting as a graph partition problem and introduce a new family of Markov chains called recombination (or ). We focus on the use of spanning trees for recombination, an idea introduced by our research group in 2018 and now in wide use in the redistricting field.