Question answering over RDF data like knowledge graphs has been greatly advanced, with a number of good systems providing crisp answers for natural language questions or telegraphic queries. Some of these systems incorporate textual sources as additional evidence for the answering process, but cannot compute answers that are present in text alone. Conversely, the IR and NLP communities have addressed QA over text, but such systems barely utilize semantic data and knowledge. This paper presents a method for complex questions that can seamlessly operate over a mixture of RDF datasets and text corpora, or individual sources, in a unified framework. Our method, called UNIQORN, builds a context graph on-the-fly, by retrieving question-relevant evidences from the RDF data and/or a text corpus, using fine-tuned BERT models. The resulting graph typically contains all question-relevant evidences but also a lot of noise. UNIQORN copes with this input by a graph algorithm for Group Steiner Trees, that identifies the best answer candidates in the context graph. Experimental results on several benchmarks of complex questions with multiple entities and relations, show that UNIQORN significantly outperforms state-of-the-art methods for heterogeneous QA - in a full training mode, as well as in zero-shot settings. The graph-based methodology provides user-interpretable evidence for the complete answering process.