A miter joint connects two beams, typically of the same cross section, at an angle such that the longitudinal beam edges continue across the joint. When more than two beams meet in one point, like in a tree, we call this a branching joint. In a branching miter joint, the beams' longitudinal edges match up properly. We survey some principles of branching miter joints. In particular, we treat joints where three beams with identical cross sections meet. These ternary miter joints can be used to construct various branching structures. We present two works of art that involve branching miter joints.