Brain computer interface (BCI) applications are emerging from the laboratory to the field environment with ever-increasing demands for high accuracy. However, enhancements in accuracy by employing multisensory devices or via hybridization techniques are inflicting issues like big data and soaring computation complexity. Such enhancements will further aggravate the miseries in the field environments. With more computational complexity and storage requirements, even the on-premise laboratory setups can face hardware and software renewal costs. In addition, it may also come across over-provisioning or under-provisioning of resources. Under such scenarios, computation offloading to cloud machines is gaining considerable attention from academia and industry. The key premise of cloud computing is that it involves the scope of on-demand resource availability and parallel processing. In addition, cloud resources can be accessed ubiquitously. With the advancements in internet technologies, portable BCI headsets can easily be integrated with cloud computing. However, inadvertent usage of cloud resources is neither beneficial for service users nor for service providers, as cloud services are paid. Hence, this paper chronologically investigates contemporary research solutions, considering where and how the cloud has been integrated with the BCI environments. In addition, it also puts forward the related challenges and the potential issues that demand future attention for the seamless integration of the cloud and BCI environment.