The need for open science has been recognized by the communities of meteorology and climate science. While these domains are mature in terms of applying digital technologies, the implementation of open science methodologies is less advanced. In a session on "Weather and Climate Science in the Digital Era"at the 14th IEEE International eScience Conference domain specialists and data and computer scientists discussed the road towards open weather and climate science. Roughly 80ĝ€¯% of the studies presented in the conference session showed the added value of open data and software. These studies included open datasets from disparate sources in their analyses or developed tools and approaches that were made openly available to the research community. Furthermore, shared software is a prerequisite for the studies which presented systems like a model coupling framework or digital collaboration platform. Although these studies showed that sharing code and data is important, the consensus among the participants was that this is not sufficient to achieve open weather and climate science and that there are important issues to address. At the level of technology, the application of the findable, accessible, interoperable, and reusable (FAIR) principles to many datasets used in weather and climate science remains a challenge. This may be due to scalability (in the case of high-resolution climate model data, for example), legal barriers such as those encountered in using weather forecast data, or issues with heterogeneity (for example, when trying to make use of citizen data). In addition, the complexity of current software platforms often limits collaboration between researchers and the optimal use of open science tools and methods. The main challenges we observed, however, were non-technical and impact the practice of science as a whole. There is a need for new roles and responsibilities in the scientific process. People working at the interface of science and digital technology - e.g., data stewards and research software engineers - should collaborate with domain researchers to ensure the optimal use of open science tools and methods. In order to remove legal boundaries on sharing data, non-academic parties such as meteorological institutes should be allowed to act as trusted agents. Besides the creation of these new roles, novel policies regarding open weather and climate science should be developed in an inclusive way in order to engage all stakeholders. Although there is an ongoing debate on open science in the community, the individual aspects are usually discussed in isolation. Our approach in this paper takes the discourse further by focusing on "open science in weather and climate research"as a whole. We consider all aspects of open science and discuss the challenges and opportunities of recent open science developments in data, software, and hardware. We have compiled these into a list of concrete recommendations that could bring us closer to open weather and climate science. We acknowledge that the development of open weather and climate science requires effort to change, but the benefits are large. We have observed these benefits directly in the studies presented in the conference and believe that it leads to much faster progress in understanding our complex world.