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Devices at the edge of wireless networks are the last mile data sources for machine learning (ML). As opposed to traditional ready-made public datasets, these user-generated private datasets reflect the freshest local environments in real time. They are thus indispensable for enabling mission-critical intelligent systems, ranging from fog radio access networks (RANs) to driverless cars and e-Health wearables. This article focuses on how to distill high-quality on-device ML models using fog computing, from such user-generated private data dispersed across wirelessly connected devices. To this end, we introduce communication-efficient and privacy-preserving distributed ML frameworks, termed fog ML (FML), wherein on-device ML models are trained by exchanging model parameters, model outputs, and surrogate data. We then present advanced FML frameworks addressing wireless RAN characteristics, limited on-device resources, and imbalanced data distributions. Our study suggests that the full potential of FML can be reached by co-designing communication and distributed ML operations while accounting for heterogeneous hardware specifications, data characteristics, and user requirements.