In the past decade, most effort in the study of supermassive black holes (BHs) has been devoted to measuring their masses. This led to the finding of the tight M_BH–σ relation, which indicates the existence of strong links between the formation of the BHs and of their host spheroids. Many scenarios have been proposed to explain this relation, and all agree on the key role of BHs' growth and feedback in shaping their host galaxies. However, the currently available observational constraints, essentially BH masses and galaxy photometry, are not sufficient to conclusively select among the alternatives. A crucial piece of information on black-hole formation is recorded in the orbital distribution of the stars, which can only be extracted from high-resolution integral-field (IF) stellar kinematics. The introduction of IF spectrographs with adaptive optics on large telescopes opens a new era in the study of BHs by finally allowing this key element to be uncovered. This information will be complementary to what will be provided by the LISA gravitational wave satellite, which can directly detect coalescing BHs. Here, an example is presented for the recovery of the orbital distribution in the centre of the giant elliptical galaxy M87, which has a well-resolved BH sphere of influence, using SAURON IF kinematics.