I will present results concerning immersed Klein bottles in euclidean n-space with low Willmore energy. Together with P. Breuning and J. Hirsch I proved that there is a smooth embedded Klein bottle that minimizes the Willmore energy among immersed Klein bottles when ngeq 4. I will shortly explain that the minimizer is probably already known: Lawson’s bipolar tildetau_{3,1}-Klein bottle, a minimal Klein bottle in S^4. If n=4, there are three distinct homotopy classes of immersed Klein bottles that are regularly homotopic to an embedding. One contains the above mentioned minimizer. The other two are characterized by the property of having Euler normal number +4 or -4. I will explain that the minimum of the Willmore energy in these two classes is 8pi. Furthermore, there are infinity many distinct embedded surfaces minimizing the Willmore energy in these classes. The proof is based on the twistor theory of the Euclidean four-space.