Superradiant instability of rotating black holes leads to the formation of extended bosonic clouds around them. These high-density environments allow for probing a large section of the parameter space for axions and other ultra-light bosons, even in the absence of their cosmological abundance. If the instability occurs in a binary system, both the orbital dynamics of the binary and the superradiant evolution of the cloud can be significantly modified. In this talk I will present a systematic way to describe this dynamics for eccentric and inclined orbits, thus correcting and extending previous results obtained in simplified settings while allowing for the inclusion of post-Newtonian effects. In particular, I will show that the presence of bosonic clouds can lead to the growth of eccentricity and the alignment of the orbital and black hole spin. These effects can drastically affect the in-band phase evolution and peak frequency, as well as change the population properties of binary black holes. In this way, LISA, along with future mid-band and Deci-hertz detectors, can be used as a probe of the ultra-light frontier of particle physics.