Container-based virtualization has gained a significant importance in a deployment of software applications in cloud-based environments. The technology fully relies on operating system features and does not require a virtualization layer (hypervisor) that introduces a performance degradation. Container-based virtualization allows to co-locate multiple isolated containers on a single computation node as well as to decompose an application into multiple containers distributed among several hosts (e.g., in fog computing layer). Such a technology seems very promising in other domains as well, e.g., in industrial automation, automotive, and aviation industry where mixed criticality containerized applications from various vendors can be co-located on shared resources.However, such industrial domains often require real-time behavior (i.e, a capability to meet predefined deadlines). These capabilities are not fully supported by the container-based virtualization yet. In this work, we provide a systematic literature survey study that summarizes the effort of the research community on bringing real-time properties in container-based virtualization. We categorize existing work into main research areas and identify possible immature points of the technology.