Abstract: I shall report about my 2011 results, which is the resolution of one long standing problem in the theory of Darboux transformations. It is known that many Darboux transformations can be constructed using Darboux Wronskian formulas. The only known exceptions have been two transformations of order one - Laplace transformations, which are often used in applications. I shall show that for order one there is no other exceptions and that for order two Wronskian formulas are complete. History of the question as well as an introduction into the area will be provided.