Blind source separation (BSS) is a well-established framework for data analysis, whose goal is to separate a number of sources from their observed mixture using the fewest assumptions. However, its potential is far from being exhausted. Recently, concepts from data fusion have opened new horizons and opportunities, such as enhanced identifiability and interpretability. In this talk, we focus on one of these novel models, called joint independent subspace analysis (JISA). JISA can be regarded as a new flexible BSS approach to data fusion, multi-set data analysis, as well as other potential applications. JISA can be reformulated as a coupled block diagonalization of a set of matrices. We present results on performance, uniqueness, and a Newton-based algorithm. We show a link with other BSS and joint matrix factorization problems. This is joint work with Christian Jutten.