Precision oncology relies on the identification of targetable molecular alterations in tumor tissues. In many tumor types, a limited set of molecular tests is currently part of standard diagnostic workflows. However, universal testing for all targetable alterations, especially rare ones, is limited by the cost and availability of molecular assays. From 2017 to 2021, multiple studies have shown that artificial intelligence (AI) methods can predict the probability of specific genetic alterations directly from conventional hematoxylin and eosin (H&E) tissue slides. Although these methods are currently less accurate than gold standard testing (e.g. immunohistochemistry, polymerase chain reaction or next-generation sequencing), they could be used as pre-screening tools to reduce the workload of genetic analyses. In this systematic literature review, we summarize the state of the art in predicting molecular alterations from H&E using AI. We found that AI methods perform reasonably well across multiple tumor types, although few algorithms have been broadly validated. In addition, we found that genetic alterations in FGFR, IDH, PIK3CA, BRAF, TP53, and DNA repair pathways are predictable from H&E in multiple tumor types, while many other genetic alterations have rarely been investigated or were only poorly predictable. Finally, we discuss the next steps for the implementation of AI-based surrogate tests in diagnostic workflows.