Spin-orbit torques arising from the spin-orbit coupling of non-magnetic heavy metals allow electrical switching of perpendicular magnetization. However, the switching is not purely electrical in laterally homogeneous structures. An extra in-plane magnetic field is indeed required to achieve deterministic switching, and this is detrimental for device applications. On the other hand, if antiferromagnets can generate spin-orbit torques, they may enable all-electrical deterministic switching because the desired magnetic field may be replaced by their exchange bias. Here we report sizeable spin-orbit torques in IrMn/CoFeB/MgO structures. The antiferromagnetic IrMn layer also supplies an in-plane exchange bias field, which enables all-electrical deterministic switching of perpendicular magnetization without any assistance from an external magnetic field. Together with sizeable spin-orbit torques, these features make antiferromagnets a promising candidate for future spintronic devices. We also show that the signs of the spin-orbit torques in various IrMn-based structures cannot be explained by existing theories and thus significant theoretical progress is required.