While in the vast majority of cases fluorescence in biological matter has been attributed to aromatic or conjugated groups, peptides associated with neurodegenerative diseases, such as Alzheimer's, Parkinson's, or Huntington's, have been recently shown to display an intrinsic visible fluorescence even in the absence of aromatic residues. This has called the attention of researchers from many different fields, trying to understand the origin of this peculiar behavior and, at the same time, motivating the search for novel strategies to control the optical properties of new biophotonic materials. Today, after nearly 15 years of its discovery, there is a growing consensus about the mechanism underlying this phenomenon, namely, that electronic interactions between non-optically active molecules can result in supramolecular assemblies that are fluorescent. Despite this progress, many aspects of this phenomenon remain uncharted territory. In this Perspective, we lay down the state-of-the-art in the field highlighting the open questions from both experimental and theoretical fronts in this fascinating emerging area of non-aromatic fluorescence.