Learning science through the process of inquiry is advocated in curriculum documents across many jurisdictions. However, a number of studies suggest that teachers struggle to help students engage in inquiry practices. This is not surprising as many teachers of science have not engaged in scientific inquiry and possibly hold naïve ideas about what constitutes scientific inquiry. This study investigates teachers' self-reported approaches to teaching science through inquiry. Phenomenographic interviews undertaken with 20 elementary teachers revealed teachers identified six approaches to teaching for inquiry, clustered within three categories. These approaches were categorized as Free and Illustrated Inquiries as part of an Experience-centered category, Solution and Method Inquiries as part of a Problem-centered category, and Topic and Chaperoned Inquiries as part of a Question-centered category. This study contributes to our theoretical understanding of how teachers approach Inquiry Teaching and suggests fertile areas of future research into this valued and influential phenomenon broadly known as "Inquiry Teaching".