Protein ubiquitination is a post-translational modification that affects many aspects of cellular processes, including the stability of proteins, activation of cellular signaling pathways and response to DNA damage. This versatility arises from the ability of ubiquitin (Ub) to form structurally and functionally distinct polymers, using one of the seven lysine residues (K6, K11, K27, K29, K33, K48, K63) or the N-terminal methionine, M1, through an enzymatic cascade involving Ub-activating (E1), Ub-conjugating (E2), and Ub-ligase (E3) enzymes. These Ub subunits can be extended in homotypic Ub chains, where all linkages are the same chain type, or heterotypic Ub chains that comprise alternating linkage types or branches. This dissertation introduces new methods for studying the formation and cleavage of branched Ub chains. Complementary approaches of biochemistry, mass spectrometry, and cell biology were utilized to 1) quantitate the formation of phosphorylated heterotypic chains, 2) elucidate the debranching activity of UCH37, and 3) detail a method in isolating specific proteasome complexes to investigate proteasomal-bound deubiquitinases. These findings contribute to the growing information about branched Ub chains that will aid in the development of biochemical strategies for studying their impact in many cellular processes.