Process systems engineering (PSE) has been an active research area for nearly seventy years and addresses multiple systems from the process industry. Among these are Process Supply Chains that can be described as interconnected sets of entities responsible for the sourcing, production and distribution of a large set of chemical and/or bio- based products. Due to the high diversity of materials, processes and information flows such networks result in highly complex systems that are very difficult to manage. The PSE community has a critical role to support the design and management of such systems through the development of tools that are able to address such complexity. Focusing initially on a real-world process supply chain, the industrial gas supply chain, this paper identifies and discusses current contributions, challenges and perspectives in process supply chains that can guide research professionals to address such challenges. In general, such challenges encompass supply chain scope representations, modeling approaches, data management and implementation. Examples include supply chain risk and uncertainty, multiscale decisions, sustainability and resiliency.