Over the past few years a new tool from algebraic geometry, called a bilinear group, has transformed public-key cryptography. Bilinear groups enable the development of a new generation of cryptosystems that solve long standing open problems in cryptography and provide brand new functionality. In this short note we give a few examples and pose a number open problems that will hopefully be resolved in the coming years. This note is intended as a partial annotated bibliography and is far from a complete survey. For simplicity, throughout this note we use terms such as "efficient algorithm" and "negligible function." These terms can be made precise using asymptotic notation, equating "efficient" with "polynomial time" and "negligible function" with "eventually less than 1/nc for all c > 0."