In recent years, partially due to the COVID-19 pandemic, scientific interest in aromatherapy has increased significantly. However, many alleged effects and mechanisms of action of essential oils need to be verified by scientific methods. The search for new bioactive compounds of plant origin is also of great importance. In this regard, we turned to in vivo studies on model organisms. We performed an initial systematic literature review of the PubMed articles on the effects of essential oil odors on behavioral responses in laboratory rats and mice. We annotated the retrieved list of 77 articles considering the type of plant source, availability of data on the chemical composition of the essential oil, species/sex/age of the experimental animal, parameters of odor exposure, model of human disorders used, and types of behavioral tests. Among the main gaps in the scientific coverage, we highlighted the imbalance in the sex and age of the laboratory animals, such as the prevalence of young males. In the referenced studies, the effects of essential oil odors on depression-like, anxiety and exploratory behavior, as well as on learning and memory were presented most fully. But the effects on social behavior of animals were rarely addressed, which we also consider a gap to be filled with future studies.