Transfer learning and meta-learning offer some of the most promising avenues to unlock the scalability of healthcare and consumer technologies driven by biosignal data. This is because current methods cannot generalise well across human subjects' data and handle learning from different heterogeneously collected data sets, thus limiting the scale of training data. On the other side, developments in transfer learning would benefit significantly from a real-world benchmark with immediate practical application. Therefore, we pick electroencephalography (EEG) as an exemplar for what makes biosignal machine learning hard. We design two transfer learning challenges around diagnostics and Brain-Computer-Interfacing (BCI), that have to be solved in the face of low signal-to-noise ratios, major variability among subjects, differences in the data recording sessions and techniques, and even between the specific BCI tasks recorded in the dataset. Task 1 is centred on the field of medical diagnostics, addressing automatic sleep stage annotation across subjects. Task 2 is centred on Brain-Computer Interfacing (BCI), addressing motor imagery decoding across both subjects and data sets. The BEETL competition with its over 30 competing teams and its 3 winning entries brought attention to the potential of deep transfer learning and combinations of set theory and conventional machine learning techniques to overcome the challenges. The results set a new state-of-the-art for the real-world BEETL benchmark.