Coded caching and coded computing have drawn significant attention in recent years due to their advantages in reducing the traffic load and in distributing computational burden to edge devices. There have been many research results addressing different aspects of these problems; however, there are still various challenges that need to be addressed. In particular, their use over wireless channels is not fully understood. With this motivation, this thesis considers these two distributed systems over wireless channels taking into account realistic channel effects as well as practical implementation constraints. In the first part of the thesis, we study coded caching over a wireless packet erasure channel where each receiver encounters packet erasures independently with the same probability. We propose two different schemes for packet erasure channels: sending the same message (SSM) and a greedy approach. Also, a simplified version of the greedy algorithm called the grouped greedy algorithm is proposed to reduce the system complexity. For the grouped greedy algorithm, an upper bound for transmission rate is derived, and it is shown that this upper bound is very close to the simulation results for small packet erasure probabilities. We then study coded caching over non-ergodic fading channels. As the multicast capacity of a broadcast channel is restricted by the user experiencing the worst channel conditions, we formulate an optimization problem to minimize the transmission time by grouping users based on their channel conditions, and transmit coded messages according to the worst channel in the group, as opposed to the worst among all. We develop two algorithms to determine the user groups: a locally optimal iterative algorithm and a numerically more efficient solution through a shortest path problem. In the second part of the thesis, we study collaborative machine learning (ML) systems, which is also known as federated learning, where a massive dataset is distributed across independent workers that compute their local gradient estimates based on their own datasets. Workers send their estimates through a multipath fading multiple access channel (MAC) with orthogonal frequency division multiplexing (OFDM) to mitigate the frequency selectivity of the channel. We assume that the parameter server (PS) employs multiple antennas to align the received signals with no channel state information (CSI) at the workers. To reduce the power consumption and hardware costs, we employ complex-valued low-resolution analog to digital converters (ADCs) at the receiver side and study the effects of practical low cost ADCs on the learning performance of the system. Our theoretical analysis shows that the impairments caused by a low-resolution ADC do not prevent the convergence of the learning algorithm, and fading effects vanish when a sufficient number of antennas are used at the PS. We also validate our theoretical results via simulations, and further, we show that using one-bit ADCs causes only a slight decrease in the learning accuracy.