A major challenge in stance detection is the large (potentially infinite) and diverse set of stance topics. Collecting data for such a set is unrealistic due to both the expense of annotation and the continuous creation of new real-world topics (e.g., a new politician runs for oce). Furthermore, stancetaking occurs in a wide range of languages and genres (e.g., Twitter, news articles). While zero-shot stance detection in English, where evaluation is on topics not seen during training, has received increasing attention, we argue that this attention should be expanded to multilingual and multi-genre settings. We discuss two paradigms for English zero-shot stance detection evaluation, as well as recent work in this area. We then discuss recent work on multilingual and multi-genre stance detection, which has focused primarily on non-zero-shot settings. We argue that this work should be expanded to multilingual and multi-genre zero-shot stance detection and propose best practices to systematize and stimulate future work in this direction. While domain adaptation techniques are well-suited for work in these settings, we argue that increased care should be taken to improve model explainability and to conduct robust evaluations, considering not only empirical generalization ability but also the understanding of complex language and inferences.