Many complex quantum phenomena require a description that goes beyond the standard paradigm of state preparations, evolutions, and measurements. A suitable framework for tackling such scenarios is that of , i.e., quantum operations that transform quantum operations. These objects are fundamental to modern quantum theory and recent years have seen a proliferation of technical and conceptual results that fundamentally rely on them; they naturally emerge in quantum circuit architectures, correlated open dynamics, and investigations of quantum causality, to name but a few fields of application. In this Tutorial, we provide a pedagogical introduction to higher-order quantum operations: we offer the tools to work with them in various contexts and firmly embed them within the current research landscape. Through this approach, our intent is to enable multiple points of access to the field, highlight the interconnectedness of distinct areas, and provide the means to meaningfully engage with state-of-the-art research developments. We conclude by identifying open problems and future research directions in this rapidly evolving field.