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A groundbreaking design of radio access networks (RANs) is needed to fulfill 5G traffic requirements. To this aim, a cost-effective and flexible strategy consists of complementing terrestrial RANs with unmanned aerial vehicles (UAVs). However, several problems must be solved in order to effectively deploy such UAV-based RANs (U-RANs). Indeed, due to the high complexity and heterogeneity of these networks, model-based design approaches, often relying on restrictive assumptions and constraints, exhibit severe limitation in real-world scenarios. Moreover, design of a set of appropriate protocols for such U-RANs is a highly sophisticated task. In this context, machine learning (ML) emerges as a useful tool to obtain practical and effective solutions. In this paper, we discuss why, how, and which types of ML methods are useful for designing U-RANs, by focusing in particular on supervised and reinforcement learning strategies.