Differential equations with "maxima"- differential equations that contain the maximum of the unknown function over a previous interval - adequately model real-world processes whose present state significantly depends on the maximum value of the state on a past time interval. More and more, these questions model and regulate the behavior of various technical systems on which our ever-advancing, high-tech world depends. Understanding and manipulating the theoretical results and investigations of differential equations with maxima opens the door to enormous possibilities for applications to real-world processes and phenomena.