The higher order free cumulants, introduced by Collins, Mingo, Śniady and Speicher in 2006, is a concept that generalizes the free cumulants and permits to define the notion of higher order freeness. In this talk we will talk about the higher order free cumulants (and their corresponding higher order moments) of a complex Wigner matrix. We will talk about previous results around the first and second order case, the first one is part of the work done by Wigner while the second one was answered by Male, Mingo, Péché and Speicher in 2020. We will also talk about the third order case which we recently solved in co-authorship with James Mingo. If time permits, we will talk about higher order cases and ongoing work.