We review the expanding, internet-enabled, and rapidly evolving field of citizen astronomy, focusing on research projects in stellar, extragalactic, and planetary science that have benefited from the participation of members of the public. These volunteers contribute in various ways: making and analyzing new observations, visually classifying features in images and light curves, exploring models constrained by astronomical data sets, and initiating new scientific enquiries. The most productive citizen astronomy projects involve close collaboration between the professionals and amateurs involved and occupy scientific niches not easily filled by great observatories or machine learning methods: Citizen astronomers are motivated by being of service to science, as well as by their interest in the subject. We expect participation and productivity in citizen astronomy to increase, as data sets get larger and citizen science platforms become more efficient. Opportunities include engaging citizens in ever-more advanced analyses and facilitating citizen-led enquiry through professional tools designed with citizens in mind.