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. these operations capture the failure of the $e_n$ multiplication to be strictly commutative, and they prove useful for computations. after reviewing the main ideas from may and cohen's work, i will discuss a framework to generalize these operations to homology with certain twisted coefficient systems and give a complete classification of twisted operations for $e_{\infty}$-algebras. i will also explain computational results that show the existence of new operations for $e_2$-algebras.