Change point analysis aims at testing, whether or not structural breaks have occurred in a given time series. The problem has received considerable attention as subsequent statistical methodology will often fail in the presence of change points. Of particular interest is methodology that is robust with respect to outliers or heavy tails, such as using U-statistics with bounded kernels. The purpose of this paper is twofold: We provide a survey of the current results in the literature on change point testing based on U-statistics in various scenarios, including a-posteriori and sequential tests for univariate time series, as well as a-posteriori tests for high-dimensional time series, both in a panel and functional setting. Secondly, we propose an alternative approach to the existing \(L_2\) -methodology for panel data, related to the Wilcoxon-Mann-Whitney U-test, derive the null distribution, and obtain some power results. We accompany these new findings by some simulations.