Abstract: In the 70s, Fred Cohen and Peter May gave a description of the mod p homology of a free $$E_n$$-algebra in terms of certain homology operations, known as Dyer–Lashof operations, and the Browder bracket. I will discuss a framework to generalize these operations to homology with certain twisted coefficient systems and give a description of the homology of a free $$E_{\infty}$$-algebra in terms of these operations. I will also give an overview of work in progress on twisted homology operations for $$E_2$$-algebras and discuss an application to mixed braid groups.