Relativization in randomness

We discuss the different contexts in which relativization occurs in randomness and the effect that the relativization chosen has on the results we can obtain. We study several characterizations of the K-trivials in terms of concepts ranging from cuppability to density, and we consider a uniform relativization for randomness that gives us more natural results for computable randomness, Schnorr randomness, and Kurtz randomness than the classical relativization does (the relativization for Martin-Löf randomness is unaffected by this change). We then evaluate the relativizations we have considered and suggest some avenues for further work.