The ever-increasing demands for both content and computation over wireless networks require moving some of the core processing capabilities close to the network edge. This dissertation considers coded caching and delivery which makes content delivery more efficient by moving content to the edge, as well as distributed learning at the network edge that can bring network intelligence close to edge devices and speed up large-scale data collection and learning problems.

First proactive content caching is studied, where a server with a library of files transmit contents to the users simultaneously. Each user requests a single file from the library and stores content in its cache with limited size proactively, before revealing the demands. The performance is first analysed in terms of the minimum number of bits transmitted by the server to satisfy the users' demands over an error-free shared link. Then, by considering various models for the shared link, physical layer aspect of fulfilling users' demands is studied. The highest achievable rate of each file in the library is characterized, upper and lower bounds on the transmit power are derived, and finally a caching system with delivering files to the users at different rates is investigated, and the rate tuples at which the requested contents can be delivered to the users is characterized.

Next machine learning (ML) at the wireless edge is studied. First, by considering scheduling of computation tasks across multiple computational nodes to compute an arbitrary function, upper and lower bounds on the minimum average completion time are developed. Then collaborative ML at the wireless edge is studied, where power and bandwidth-limited wireless devices with local datasets carry out a learning task with the help of a remote parameter server (PS). Digital and analog approaches are introduced for transmission from the users to the PS over a shared wireless medium.