This paper considers two families of methods allowing to get interpretable factors without imposing their interpretation a priori: factor rotations and sparse PCA. Monte Carlo simulations show their performance in recovering the correct factor structure. In an empirical application with a large U.S. macroeconomic dataset, they recover the same factor structure, offering a clear economic interpretation. This factor representation seems more natural and informative than competitors, offering new lens to disentangle the driving forces within a factor model. In particular, the structural instability appears to be more limited, and of different nature than what was previously found.