Reactive local algorithms are distributed algorithms which suit the needs of battery-powered, large-scale wireless ad hoc and sensor networks particularly well. By avoiding both unnecessary wireless transmissions and proactive maintenance of neighborhood tables (i.e., beaconing), such algorithms minimize communication load and overhead, and scale well with increasing network size. This way, resources such as bandwidth and energy are saved, and the probability of message collisions is reduced, which leads to an increase in the packet reception ratio and a decrease of latencies. Currently, the two main application areas of this algorithm type are geographic routing and topology control, in particular the construction of a node's adjacency in a connected, planar representation of the network graph. Geographic routing enables wireless multi-hop communication in the absence of any network infrastructure, based on geographic node positions. The construction of planar topologies is a requirement for efficient, local solutions for a variety of algorithmic problems. This thesis contributes to reactive algorithm research in two ways, on an abstract level, as well as by the introduction of novel algorithms: For the very first time, reactive algorithms are considered as a whole and as an individual research area. A comprehensive survey of the literature is given which lists and classifies known algorithms, techniques, and application domains. Moreover, the mathematical concept of O- and Omega-reactive local topology control is introduced. This concept unambiguously distinguishes reactive from conventional, beacon-based, topology control algorithms, serves as a taxonomy for existing and prospective algorithms of this kind, and facilitates in-depth investigations of the principal power of the reactive approach, beyond analysis of concrete algorithms. Novel reactive local topology control and geographic routing algorithms are introduced under both the unit disk and quasi unit disk graph model. These algorithms compute a node's local view on connected, planar, constant stretch Euclidean and topological spanners of the underlying network graph and route messages reactively on these spanners while guaranteeing the messages' delivery. All previously known algorithms are either not reactive, or do not provide constant Euclidean and topological stretch properties. A particularly important partial result of this work is that the partial Delaunay triangulation (PDT) is a constant stretch Euclidean spanner for the unit disk graph. To conclude, this thesis provides a basis for structured and substantial research in this field and shows the reactive approach to be a powerful tool for algorithm design in wireless ad hoc and sensor networking.