Edge devices collect massive amounts of data, opening up new potentials for machine learning applications. Machine learning at the edge can benefit from exploiting both data and processing power distributed across many wireless devices, but this brings about many new challenges including the low latency requirements of learning applications, privacy concerns preventing data sharing, and the impact of noise and interference on the convergence of the learning process. Overcoming these challenges while meeting the requirements of the machine learning tasks calls for a new paradigm of semantic-oriented communication network design tailored for learning applications. In this talk, I will present recent results on efficient distributed inference and training over wireless networks taking into account channel impairments and power and bandwidth limitations of wireless devices, as well as the semantics of the underlying learning tasks. This will involve bringing together novel communication and coding techniques with distributed learning and inference algorithms.