Recent years have seen significant growth in the cloud computing market, both in terms of provider competition (including private offerings) and customer adoption. However, the cloud computing world still lacks adopted standard programming interfaces, which has a knock-on effect on the costs associated with interoperability and severely limits the flexibility and portability of applications and virtual infrastructures. This has brought about an increasing number of cross-cloud architectures, i.e. systems that span across cloud provisioning boundaries. This position paper condenses discussions from the CrossCloud event series to outline the types of cross-cloud systems and their associated design decisions, and laments challenges and opportunities they create.