The proteasome, a multiprotease complex, is clinically validated as an anticancer target by the FDA approval of bortezomib and carfilzomib for the treatment of multiple myeloma. The emergence of resistance to proteasome inhibitors however remains a major clinical challenge. Recently, distinct types of proteasomes termed ‘intermediate proteasomes’, which contain unconventional mixtures of catalytic subunits, have been implicated with drug resistance of tumor cells. In elucidating the role of intermediate proteasomes in drug resistance, a crucial step is to unequivocally determine the subunit composition of intermediate proteasomes in cells. With this in mind, the goal of the studies reported in this dissertation is to develop novel chemical tools which can facilitate the investigation of intermediate proteasomes via two complementary approaches: a FRET-based approach and a bifunctional cross-linking approach. Chapter 2 describes the structure-based design, synthesis, and characterization of a peptide epoxyketone-based fluorescent probe, named as LKS01-B650, which selectively targets the immunoproteasome subunit β5i/LMP7. In addition to its utility in determining the identity of intermediate proteasomes as FRET-based probe, this imaging agent may also serve as a valuable tool in visualizing the immunoproteasome in living cells. Chapter 3 describes the design and synthesis of various epoxyketone-based bifunctional agents. The ability of these bifunctional agents to cross-link different catalytic subunits within a proteasome complex is shown by mobility shift assays.These bifunctional agents may provide important information in determining the subunit composition of proteasomes. Chapter 4 describes a systematic study of the relationship between the proteasome inhibitor structure and the inhibitory activity against critical subunits of the proteasome. Given the reported role of β5i/LMP7 in autoimmune diseases, this study may provide useful insights in developing therapeutic agents for autoimmune diseases as well as other diseases. Chapter 5 describes a separate study which is not related to proteasome biology. A concise approach to synthesize 1-azaspirocyclic ring systems is developed by utilizing a novel semi-pinacol/Beckmann rearrangement. Additionally, an environmentally benign, microwave-assisted, and solvent-free self-condensation of carbonyl compounds is reported.