What is the scientific study of butterflies and moths called?

The scientific study of butterflies and moths is called lepidopterology.

Lepidopterology is a branch of entomology, the broader study of insects. Researchers in this field investigate classification, evolution, behavior, ecology, physiology, life cycles, and conservation across Lepidoptera.

The word is based on Lepidoptera, the insect order containing butterflies and moths. A person who studies these insects may be called a lepidopterist. Professional scientists and serious amateur naturalists both contribute records, collections, and observations.

Lepidopterology is broader than butterfly watching. It includes nocturnal moth surveys, caterpillar host-plant research, migration studies, taxonomy, and analysis of wing scales. Entomology is therefore a correct broad description of the field, but lepidopterology is the specific term requested here.