We recall some basic computations in the Milnor-Witt K-theory of a field, following Morel. We then focus on the Witt K-theory of a field of characteristic two and give an elementary proof of the fact that it is isomorphic as a graded ring to the Rees algebra of the fundamental ideal of the Witt ring of symmetric bilinear forms using Kato's solution to Milnor's conjecture on quadratic form.