Although classified more than 30 years ago, narrow-line Seyfert 1 galaxies (NLS1s) have moved into the spotlight during the last decade, after the discovery of gamma-ray emission and relativistic jets in some of them. In this seminar I will outline the main physical properties of NLS1s, and discuss their role in the framework of AGN unified models. I will also present the recent discovery of Jy- level flares at 37 GHz at the Metsähovi Radio Observatory, detected in a subset of NLS1s previously classified as radio-quiet or radio-silent. This unexpected finding suggested that a population of absorbed relativistic jets may be hidden in this class (and perhaps in other classes) of AGN, and showed once more the weaknesses of the still-too-widely-used radio-loudness criterion. I will finally discuss the most recent developments of our research, along with its far-reaching implications.