Bioactive peptides derived from enzymatic hydrolysis are gaining attention for the production of supplements, pharmaceutical compounds, and functional foods. However, their inclusion in oral delivery systems is constrained by their high susceptibility to degradation during human gastrointestinal digestion. Encapsulating techniques can be used to stabilize functional ingredients, helping to maintain their activity after processing, storage, and digestion, thus improving their bioaccessibility. Monoaxial spray-drying and electrospraying are common and economical techniques used for the encapsulation of nutrients and bioactive compounds in both the pharmaceutical and food industries. Although less studied, the coaxial configuration of both techniques could potentially improve the stabilization of protein-based bioactives via the formation of shell–core structures. This article reviews the application of these techniques, both monoaxial and coaxial configurations, for the encapsulation of bioactive peptides and protein hydrolysates, focusing on the factors affecting the properties of the encapsulates, such as the formulation of the feed solution, selection of carrier and solvent, as well as the processing conditions used. Furthermore, this review covers the release, retention of bioactivity, and stability of peptide-loaded encapsulates after processing and digestion.