  We give a survey of basic results on the cut norm and cut metric for graphons
(and sometimes more general kernels), with emphasis on the equivalence problem.
The main results are not new, but we add various technical complements, and a
new proof of the uniqueness theorem by Borgs, Chayes and Lov\'asz. We allow
graphons on general probability spaces whenever possible. We also give some new
results for {0,1}-valued graphons and for pure graphons.
