The emerging beyond 5G/6G networks come with novel, latency-sensitive and computation-intensive applications that require enhanced network performance and infrastructure to meet the expected quality of experience for end users. To cope with this challenge, computation offloading leverages the benefits of multi-access edge computing to migrate the application tasks requiring additional computing resources for reduced execution delay. Although the benefits of introducing offloading mechanisms into the network might be straightforward, the implementation is not trivial due to various communication and computation trade-offs that must be made to obtain optimal offloading decisions. In this paper, we provide an overview of computation offloading with highlight on the networking perspective by looking at different offloading decisions, current research efforts, as well as the challenges that may be encountered while building an efficient and robust offloading mechanism. In addition, we provide our view on the evolution of computation offloading in 6G networks to support novel applications through enriched infrastructure and powerful artificial intelligence techniques.