Reproducible research is often perceived as a technological challenge, but it is rooted in the challenge to improve scholarly communication in an age of digitization. When computers become involved and researchers want to allow other scientists to inspect, understand, evaluate, and build on their work, they need to create a research compendium that includes the code, data, computing environment, and script-based workflows used. Here, we present the state of the art for approaches to reach this degree of computational reproducibility, addressing literate programming and containerization while paying attention to working with geospatial data (digital maps, geographic information systems). We argue that all researchers working with computers should understand these technologies to control their computing environment, and we present the benefits of reproducible workflows in practice. Example research compendia illustrate the presented concepts and are the basis for challenges specific to geography and geosciences. Based on existing surveys and best practices from different scientific domains, we conclude that researchers today can overcome many barriers and achieve a very high degree of reproducibility. If the geography and geosciences communities adopt reproducibility and the underlying technologies in practice and in policies, they can transform the way researchers conduct and communicate their work toward increased transparency, understandability, openness, trust, productivity, and innovation.