The origins of our nearly ten-year research program of chemical and biological investigations into peptides based on homologated proteinogenic amino acids are described. The road from the biopolymer poly[ethyl (R)-3-hydroxybutanoate] to the beta-peptides was primarily a step from organic synthesis methodology (the preparation of enantiomerically pure compounds (EPCs)) to supramolecular chemistry (higher-order structures maintained through non-covalent interactions). The performing of biochemical and biological tests on the beta- and gamma-peptides, which differ from natural peptides/proteins by a single or two additional CH(2) groups per amino acid, then led into bioorganic chemistry and medicinal chemistry. The individual chapters of this review article begin with descriptions of work on beta-amino acids, beta-peptides, and polymers (Nylon-3) that dates back to the 1960s, even to the times of Emil Fischer, but did not yield insights into structures or biological properties. The numerous, often highly physiologically active, or even toxic, natural products containing beta- and gamma-amino acid moieties are then presented. Chapters on the preparation of homologated amino acids with proteinogenic side chains, their coupling to provide the corresponding peptides, both in solution (including thioligation) and on the solid phase, their isolation by preparative HPLC, and their characterization by mass spectrometry (HR-MS and MS sequencing) follow. After that, their structures, predominantly determined by NMR spectroscopy in methanolic solution, are described: helices, pleated sheets, and turns, together with stack-, crankshaft-, paddlewheel-, and staircase-like patterns. The presence of the additional C--C bonds in the backbones of the new peptides did not give rise to a chaotic increase in their secondary structures as many protein specialists might have expected: while there are indeed more structure types than are observed in the alpha-peptide realm - three different helices (10/12-, 12-, and 14-helix) if we include oligomers of trans-2-aminocyclopentanecarboxylic acid, for example - the structures are already observable with chains made up of only four components, and, having now undergone a learning process, we are able to construct them by design. The structures of the shorter beta-peptides can also be reliably determined by molecular-dynamics calculations (in solution; GROMOS program package). Unlike in the case of the natural helices, these compounds' folding into secondary structures is not cooperative. In beta- and gamma-peptides, it is possible to introduce heteroatom substituents (such as halogen or OH) onto the backbones or to incorporate heteroatoms (NH, O) directly into the chain, and, thanks to this, it has been possible to study effects unobservable in the world of the alpha-peptides. Tests with proteolytic enzymes of all types (from mammals, microorganisms, yeasts) and in vivo examination (mice, rats, insects, plants) showed beta- and gamma-peptides to be completely stable towards proteolysis and, as ...