Cloud-based architectures are advantageous in aspects such as scalability, reliability and resource utilization efficiency, to name just a few, thus being considered one of the pillars of Industry 4.0. However, in this domain, cloud computing platforms are subject to specific requirements, namely in what concerns real-time performance, determinism and fault-tolerance. This paper focuses on cloud native computing, which is an emerging and promising cloud-computing paradigm, specifically addressing its applicability to real-time systems. Firstly, it introduces the architecture of cloud native applications, discussing their principles, potential advantages and challenges. Then it addresses the opportunities and constraints of such technologies when applied to industrial real-time systems