Peptides represent an important class of biologically active molecules with high potential for the development of diagnostic and therapeutic agents due to their structural diversity, favourable pharmacokinetic properties, and synthetic availability. However, the widespread use of peptides and conjugates thereof in clinical applications can be hampered by their low stability in vivo due to rapid degradation by endogenous proteases. A promising approach to circumvent this potential limitation includes the substitution of metabolically labile amide bonds in the peptide backbone by stable isosteric amide bond mimetics. In this review, we focus on the incorporation of 1,4-disubstituted 1,2,3-triazoles as amide bond surrogates in linear peptides with the aim to increase their stability without impacting their biological function(s). We highlight the properties of this heterocycle as a trans-amide bond surrogate and summarise approaches for the synthesis of triazole-containing peptidomimetics via the Cu(I)-catalysed azide-alkyne cycloaddition (CuAAC). The impacts of the incorporation of triazoles in the backbone of diverse peptides on their biological properties such as, e.g., blood serum stability and affinity as well as selectivity towards their respective molecular target(s) are discussed.