Automated eye tracking has emerged as a powerful method in psychology, and has special benefits when studying infant populations. The field has developed much during the last decades, and while there are numerous reviews on methodological aspects and specific research topics, a general overview of the state and trends of the field has been lacking. That lack leaves the field unguided on several important aspects such as WEIRDness, statistical power and replication issues, unexploited areas of research, and the current status of the field as a whole. We here conducted a systematic review of the complete peer-reviewed English literature on automated eye tracking with children during their first two years of life (793 articles), and extracted dates of publication, author and population geographic affiliation, keywords and sample sizes. The results show that automated eye tracking in infant research is increasingly used, and is accompanied by larger sample sizes, which together suggests improved accessibility. There is a focus on WEIRD populations, and a few broad research topics (methods, language and attention) and specific topics (autism, faces) are dominating the field. The current focus leaves many areas of research understudied, yielding a large potential for more infant eye tracking in the future.