Cross-collaboration processes are decentralized by nature and their centralized monitoring can trigger mistrust. Nevertheless, a decentralized monitoring facility such as a blockchain-based and Internet-of-Things-aware (IoT-aware) business process management system can reduce this pitfall. However, concerns related to usability, privacy, and performance, hamper the wide adoption of these systems. To better understand the challenges at stake, this paper reviews the use of blockchain and IoT devices in cross-collaboration processes. This survey sheds some light on standard uses such as model engineering or permissioned blockchains which help adopt cross-collaboration business process management systems. Moreover, with respect to process design, two schools of thought coexist, addressing both constrained and loosely processes. Furthermore, a focus on data-centric processes appears to get some momentum, as many industries go digital. Finally, this survey underlines the need to orient future research towards a more flexible, scalable, and data-aware blockchain-based business process management system.