The unprecedented increase in the demand for mobile data, fuelled by new emerging applications and usecases such as high-definition video streaming and heightened online activities has caused massive strain on the existing cellular networks. As a solution, the fifth generation (5G) of cellular technology has been introduced to improve network performance through various innovative features such as millimeter-wave spectrum and Heterogeneous Networks (HetNet). In essence, HetNets include several small cells underlaid within macro-cell to serve densely populated regions like stadiums, shopping malls, and so on. Recently, a mobile layer of HetNet has been under consideration by the researchers and is often referred to as moving networks. Moving networks comprise of mobile cells that are primarily introduced to improve Quality of Service (QoS) for commuting users inside public transport because the QoS is deteriorated due to vehicular penetration losses and high Doppler shift. Furthermore, the users inside fast moving public transport also exert excessive load on the core network due to large group handovers. To this end, mobile cells will play a crucial role in reducing overall handover count and will help in alleviating these problems by decoupling in-vehicle users from the core network. This decoupling is achieved by introducing separate in-vehicle access link, and out-of-vehicle backhaul links with the core network. Additionally sidehaul links will connect mobile cells with their neighbors.To date, remarkable research results have been achieved by the research community in addressing challenges linked to moving networks. However, to the best of our knowledge, a discussion on moving networks and mobile cells in a holistic way is missing in the current literature. To fill the gap, in this paper, we comprehensively survey moving networks and mobile cells. We cover the technological aspects of moving cells and their applications in the futuristic applications. We also discuss the use-cases and value additions that moving networks may bring to future cellular architecture and identify the challenges associated with them. Based on the identified challenges we discuss the future research directions.