From prehistoric times onward, people have always found ways to incorporate mathematical thinking into art. Today, we have sophisticated mathematical machinery that we can use both to understand the rules that underlie historical patterns and to describe new designs of great beauty and originality. Better yet, computers can serve as a powerful artistic tool, helping make these mathematical visions a reality. This talk will explore some of the exciting contemporary work that lies in the intersection of mathematics and art. We will survey the creations of artists and mathematicians, working alone or in collaboration.