Self-assembly of peptides can yield an array of well-defined nanostructures that are highly attractive nanomaterials for many biomedical applications such as drug delivery. Some of the advantages of self-assembled peptide nanostructures over other delivery platforms include their chemical diversity, biocompatibility, high loading capacity for both hydrophobic and hydrophilic drugs, and their ability to target molecular recognition sites. Furthermore, these self-assembled nanostructures could be designed with novel peptide motifs, making them stimuli-responsive and achieving triggered drug delivery at disease sites. The goal of this work is to present a comprehensive review of the most recent studies on self-assembled peptides with a focus on their “smart” activity for formation of targeted and responsive drug-delivery carriers.