The dominant approach in offering cloud services is based on homogeneous commodity resources: large numbers of inexpensive machines, interconnected by off-the-shelf networking equipment, supported by stock disk drives. This is consistent with the predominant business model for data centre cloud computing, which leverages homogeneous computation, communication, and storage to provide low-cost application hosting.However, cloud service providers have reached a limit in satisfying performance and cost requirements for important classes of applications, such as geo-exploration and real-time business analytics. In particular, their platforms cannot benefit from the revolution in new hardware and network technologies for computation, communication, and storage, such as FPGAs, GPGPUs, programmable routers, and SSDs, which promise vastly increased performance, reduced energy consumption, and lower cost profiles. Their heterogeneity and complexity makes integrating them into the platform a fundamental challenge.The HARNESS project aims to bring these innovative resources into cloud platforms through a rich programme of research, validated by commercial and open source case studies. The innovations brought by HARNESS include: precise models describing requirements, policies, and expected performance of heterogeneous hardware and network resources; new virtualisation techniques tailored to these resources for flexible allocation and reallocation; advanced techniques for optimising cost/performance allocation trade offs, including spot pricing; an integrated, next-generation platform service (PaaS) for cloud-hosted applications, extending upon but compatible with existing standards; and software engineering principles for enabling applications to take full advantage of heterogeneous hardware and network resources.Through industry-led validation use cases, HARNESS demonstrates the impact that flexible and seamless heterogeneous cloud computing can have in the marketplace.