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Cell planning (CP) is the most important phase in the life cycle of a cellular system as it determines the operational expenditure, capital expenditure, as well as the long-term performance of the system. Therefore, it is not surprising that CP problems have been studied extensively for the past three decades for all four generations of cellular systems. However, the fact that small cells, a major component of future networks, are anticipated to be deployed in an impromptu fashion makes CP for future networks vis-a-vis 5G a conundrum. Furthermore, in emerging cellular systems that incorporate a variety of different cell sizes and types, heterogeneous networks (HetNets), energy efficiency, self-organizing network features, control and data plane split architectures (CDSA), massive multiple input multiple out (MIMO), coordinated multipoint (CoMP), cloud radio access network, and millimetre-wave-based cells plus the need to support Internet of Things (IoT) and device-to-device (D2D) communication require a major paradigm shift in the way cellular networks have been planned in the past. The objective of this paper is to characterize this paradigm shift by concisely reviewing past developments, analyzing the state-of-the-art challenges, and identifying future trends, challenges, and opportunities in CP in the wake of 5G. More specifically, in this paper, we investigate the problem of planning future cellular networks in detail. To this end, we first provide a brief tutorial on the CP process to identify the peculiarities that make CP one of the most challenging problems in wireless communications. This tutorial is followed by a concise recap of past research in CP. We then review key findings from recent studies that have attempted to address the aforementioned challenges in planning emerging networks. Finally, we discuss the range of technical factors that need to be taken into account while planning future networks and the promising research directions that necessitates the paradigm shift to do so.