Interrogating biological systems is often limited by access to biological probes. The emergence of "click chemistry" has revolutionized bioconjugate chemistry by providing facile reaction conditions amenable to both biologic molecules and small molecule probes such as fluorophores, toxins, or therapeutics. One particularly popular version is the copper-catalyzed azide-alkyne cycloaddition (AAC) reaction, which has spawned new alternatives such as the strain-promoted azide-alkyne cycloaddition reaction, among others. This focused review highlights practical approaches to AAC reactions for the synthesis of peptide or protein bioconjugates and contrasts current challenges and limitations in light of recent advances in the field. The conical success of antibody drug conjugates has expanded the toolbox of linkers and payloads to facilitate practical applications of bioconjugation to create novel therapeutics and biologic probes. The AAC reaction in particular is poised to enable a large set of functionalized molecules as a combinatorial approach to high-throughput bioconjugate generation, screening, and honing of lead compounds.