Operations on K-theory, such as Adams and lambda operations, have been useful in a plethora of different subjects. In the context of higher algebraic K-theory, defining them is not easy and over the last few decades many authors have envisioned constructions of them that employ highly non-trivial algebraic and homotopical methods (or both). After a short introduction, I will focus on some recent methods that have been developed in order to construct operations on higher algebraic K-theory (and on some facts in algebraic geometry of independent interest that are needed for them) and I will discuss how it is possible to show that many a priori different definitions of them agree (this is joint with B. Koeck).