What is a PCT patent application, and how does it lead into the US or EU?

A PCT (Patent Cooperation Treaty) application is a single international filing that reserves your right to seek patent protection in over 150 member countries, without committing to any of them yet. You have up to 30 months from your earliest priority date to enter the national phase in the US through the USPTO, or the regional phase in the EU through the EPO (31 months for EPO entry). It does not grant a single international patent. The USPTO and EPO each examine and grant separately. Entering the EPO regional phase via PCT usually skips a supplementary EPO search if the EPO already acted as the International Searching Authority, which is common for US, Japanese, and Chinese applicants. An International Search Report and Written Opinion produced during the PCT phase give an early read on patentability before national or regional phase costs are committed in either market.

Sources: WIPO, PCT: The International Patent System, USPTO, Patent basics.