About 20 years ago, ordinal patterns have been introduced as a simple, robust, and flexible tool for analyzing the serial dependence structure of univariate real-valued stochastic processes and dynamical systems. If applied to continuously distributed processes, one can derive nonparametric tests of the null hypothesis that the process is independent and identically distributed. Recently, also more sophisticated tasks for dependence tests have been considered: serial dependence in a discrete-valued process, the sequential monitoring of serial dependence, cross dependence in a multivariate process, and spatial dependence in a random field. This chapter provides a survey of these approaches and concludes by outlining perspectives for future research.