Federated Learning (FL) has been a promising approach to training machine learning models over decentralized edge devices without revealing data to central points. Although promising, FL’s computational overhead is a limitation, especially in resource-constrained environments. In this paper, we perform a thorough survey of techniques to reduce the computational overhead of FL. We examine algorithmic improvement, model compression methods, client selection strategies, and communication-efficient protocols that all reduce the computational overhead. We also examine the trade-offs in computation, communication, and model accuracy in varied FL environments and hardware resources. By synthesizing the existing literature and gaps in the literature, this work provides engineering insights and future work directions to design efficient and scalable FL systems deployable in heterogeneous edge environments.