Multi-access Edge Computing (MEC) is a novel edge computing paradigm that moves cloudbased processing and storage capabilities closer to mobile users by implementing server resources in the access nodes. MEC helps fulfill the stringent requirements of 5G and beyond networks to offer anytimeanywhere connectivity for many devices with ultra-low delay and huge bandwidths. Information-Centric Networking (ICN) is another prominent network technology that builds on a content-centric network architecture to overcome host-centric routing/operation shortcomings and to realize efficient pervasive and ubiquitous networking. It is envisaged to be employed in Future Internet including Beyond 5G (B5G) networks. The consolidation of ICN with MEC technology offers new opportunities to realize that vision and serve advanced use cases. However, various integration challenges are yet to be addressed to enable the wide-scale co-deployment of ICN with MEC in future networks. In this paper, we discuss and elaborate on ICN MEC integration to provide a comprehensive survey with a forward-looking perspective for B5G networks. In that regard, we deduce lessons learned from related works (for both 5G and B5G networks). We present ongoing standardization activities to highlight practical implications of such efforts. Moreover, we render key B5G use cases and highlight the role for ICN MEC integration for addressing their requirements. Finally, we layout research challenges and identify potential research directions. For this last contribution, we also provide a mapping of the latter to ICN integration challenges and use cases.