Narrow-line Seyfert 1 (NLS1) galaxies are a subclass of active galactic nuclei (AGN) identified 40 years ago, but still not well understood. NLS1s are characterized by rapid accretion onto an intermediate-mass supermassive black hole and are believed to be in an early phase of AGN evolution. Interestingly, but perhaps not surprisingly, a large fraction of the JWST-detected AGN in the early Universe could be classified as NLS1s, making understanding the local population more important than ever. In this talk, I will give a brief overview of their story so far, including some disagreements along the way, and present some of the current issues and how we intend to solve them.