Arterial delivery relies on the safe use of steerable and non-thrombogenic catheters. When necessary, balloon-tipped catheters should be able to control the blood flow and deliver drugs. This chapter describes the detailed development of transvascular catheter technology. It narrates the engineering concerns, the selection of materials, and the evolution of catheter placement technology. Most early catheter development arose for cardiac interventions later applied to neuroradiology. The foundational cardiac experience is highly relevant for future neurological applications. This chapter reviews both cardiac and neurological catheter development. It comprehensively examines the underlying physics, chemistry, and biological issues in catheter technology development, from its humble roots in urology to the future treatment of neurological diseases aided by nanotechnologies and robotics.