Blockchain interoperability, which allows state transitions across different blockchain networks, is critical functionality to facilitate major blockchain adoption. Existing interoperability protocols mostly focus on atomic token exchanges between blockchains. However, as blockchains have been upgraded from passive distributed ledgers into programmable state machines (thanks to smart contracts), the scope of blockchain interoperability goes beyond just token exchanges. In this paper, we present HyperService, the first platform that delivers interoperability and programmability across heterogeneous blockchains. HyperService is powered by two innovative designs: (i) a developer-facing programming framework that allows developers to build cross-chain applications in a unified programming model; and (ii) a secure blockchain-facing cryptography protocol that provably realizes those applications on blockchains. We implement a prototype of HyperService in approximately 35,000 lines of code to demonstrate its practicality. Our experiments show that (i) HyperService imposes reasonable latency, in order of seconds, on the end-to-end execution of cross-chain applications; (ii) the HyperService platform is scalable to continuously incorporate new large-scale production blockchains.