As three-dimensional (3D) printing technology is fast becoming more affordable and accessible, calculus instructors can now consider using 3D printing and 3D printed models to actively engage students in core concepts relating to objects in R[superscript 3]. This article describes three lessons for a multivariable calculus class in which students interact with 3D models to learn concepts relating to surfaces, solids, and multivariable functions. With each lesson are discussions and examples of student work based on the author's experience. Finally, the article includes a brief section on practical considerations for mathematics instructors thinking of using 3D printing technology in their classrooms.