Abstract：Geometric and holonomic quantum computation utilizes intrinsic geometric properties of quantum-mechanical state spaces to realize quantum logic gates. Since both geometric phases and quantum holonomies are global quantities depending only on the evolution paths of quantum systems, quantum gates based on them possess built-in resilience to certain kinds of errors. In this talk, we provide an introduction to the topic as well as give an overview of the theoretical and experimental progress for constructing geometric and holonomic quantum gates and how to combine them with other error-resistant techniques.