A one-weight code, or constant-weight code, is an error-correcting code in which all codewords share the same weight. In 1984, Bonisoli provided a classification of one-weight linear codes by leveraging the connection between codes equipped with the Hamming metric and projective systems. More recently, similar geometric techniques have been applied to the study of linear codes in the rank metric. In this talk, we discuss one-weight linear rank-metric codes, by exploiting a new geometric framework. This is a joint work with Martino Borello and Alessandro Neri.