The work described in this thesis deals with the cross- and multi-lingual detection and extraction of adverse drug reactions in biomedical texts written by laypeople. This includes the design and creation of a multi-lingual corpus, exploring ways to collect data without harming users' privacy and investigating whether cross-lingual data can mitigate class imbalance in document classification. It further addresses the question of whether zero- and cross-lingual learning can be successful in medical entity detection across languages. I describe the creation of a new tri-lingual corpus (German, French, Japanese) focusing on German and French, including the development of annotation guidelines applicable to any language and oriented towards user-generated texts. I further describe the annotation process and give an overview of the resulting dataset. The data is provided with annotations on four levels: document-level, for describing if a text contains ADRs or not; entity level for capturing relevant expressions; attribute level to further specify these expressions; The last level annotates relations to extract information on how the aforementioned entities interact. I then discuss the topic of user privacy in data about health-related issues and the question of how to collect such data for research purposes without harming the person's privacy. I provide a prototype study of how users react when they are directly asked about their experiences with ADRs. The study reveals that most people do not mind describing their experiences if asked, but that data collection might suffer from too many questions in the questionnaire. Next, I analyze the results of a potential second way of collecting social media data: the synthetic generation of pseudo-tweets based on real Twitter messages. In the analysis, I focus on the challenges this approach entails and find, despite some preliminary cleaning, that there are still problems to be found in the translations, both with respect to the meaning of the text and the annotated labels. I, therefore, give anecdotal examples of what can go wrong during automatic translation, summarize the lessons learned, and present potential steps for improvements. Subsequently, I present experimental results for cross-lingual document classification with respect to ADRs in English and German. For this, I fine-tuned classification models on different dataset configurations first on English and then on German documents, complicated by the strong label imbalance of either language's dataset. I find that incorporating English training data helps in the classification of relevant documents in German, but that it is not enough to mitigate the natural imbalance of document labels efficiently. Nevertheless, the developed models seem promising and might be particularly useful for collecting more texts describing experiences about side effects to extend the current corpus and improve the detection of relevant documents for other languages. Next, I describe my participation in the n2c2 2022 shared task of medication detection which is then extended from English to German, French and Spanish using datasets from different sub-domains based on different annotation guidelines. I show that the multi- and cross-lingual transfer works well but also strongly depends on the annotation types and definitions. After that, I re-use the discussed models to show some preliminary results on the presented corpus, first only on medication detection and then across all the annotated entity types. I find that medication detection shows promising results, especially considering that the models were fine-tuned on data from another sub-domain and applied in a zero-shot fashion to the new data. Regarding the detection of other medical expressions, I find that the performance of the models strongly depends on the entity type and propose ways to handle this. Lastly, the presented work is summarized and future steps are discussed.