Some embodiments of percutaneous ventricular assist devices have a two-part design that includes a housing component and a separately deployable rotatable inner catheter component. The housing component can include an expandable pump housing. The inner catheter can include an expandable pump impeller and an associated flexible drive shaft. The drive shaft can be coupled to a motor located external to the patient. The motor can rotate the drive shaft to spin the pump impeller inside of the pump housing, causing blood to be pumped within the patient. In some embodiments, the pump impeller is inflatable or self-expandable. The two-part percutaneous ventricular assist devices with inflatable or self-expandable pump impellers are designed to have very small delivery profiles. Accordingly, various deployment modalities, including radial artery deployment, are practicable using the two-part percutaneous ventricular assist devices described herein.