In recent years, with the availability of massive and inexpensive commodity servers, distributed computing has emerged as a promising direction for speeding up large-scale machine learning and data analysis. To deal with communication bottlenecks and security issues in distributed computing, modern state-of-the-art technologies use coding techniques. This thesis considers coding design for three different scenarios. The first scenario considers heterogeneous multi-cloud systems for distributed storage and computing in the presence of cloud collusion and failures. A capacity-achieving code is designed for matrix multiplication, and the fundamental tradeoff between code rate and computation time is characterized and shown to deteriorate when the system becomes more heterogeneous. The second scenario considers a generalization of MapReduce framework called τ-group systems. For 1-group and 2-group systems, codes are designed and performance bounds are obtained. The 1-group system is extended to edge computing over unreliable, insecure device-to-device (D2D) wireless networks. To improve reliability, we build a ρ-replication system, where each device has ρ replicas with duplicate data, and design a coded computation scheme to achieve the minimum communication load of the system and ensure weak security of wireless transmissions during data exchange. The third scenario focuses on a popular computing task called federated learning over wireless D2D networks. By carefully designing the consensus coefficients of the learning algorithm, a network coding scheme is crafted to speed up wireless decentralized learning without consuming more radio power.