Math Circles are designed to allow students to explore mathematics using a problem-solving/inquiry approach. Many of the students attending our Math Circle are mathematically talented and curious. This study examines the perspectives of the students and their families in determining why students attend Math Circle, what they enjoy about Math Circle, and what they perceive as differences in Math Circle from their classroom mathematics instruction. Findings indicate that students and parents feel that our Math Circle offers more challenging work than students are finding in their regular classroom and that the Math Circle provides a scholarly camaraderie among participants.