This CAREER project is motivated by the exponential rise in the volume of data being processed for knowledge discovery applications, such as business process optimization, healthcare analytics, cybersecurity, and scientific computing. To speed up computation, there is an increasing interest in distributed computation; however, distributing a computational task over multiple heterogeneous machines involves data movement between machines leading to communication bottlenecks, significantly impacting the time for computation. By reducing the cost and time for distributed computation, the research outcomes can have a significant and immediate economic benefit as well as a lasting societal impact. The research objectives of this project are strongly interconnected with educational components and outreach activities, which include undergraduate research involvement, interdisciplinary curriculum development, outreach to K-12 in collaboration with SARSEF (Southern Arizona Research, Science and Engineering Foundation), and raising STEM awareness through the STEM learning center and the Arizona Science, Engineering, and Mathematics (ASEM) scholars mentoring program. To enable communication-efficient distributed computation, this CAREER project will pursue the following intertwined research objectives. The first research objective is to make distributed data shuffling communication-efficient through novel coded data delivery mechanisms, that are adaptable to the underlying topology and can cope with the temporal nature of computational tasks. The second research objective is to reduce the impact of computational heterogeneity by novel work exchange algorithms through intermediate communication while minimizing the time for computation. The third research objective complements the first two in characterizing fundamental information theoretic limits by developing lower bounds on the communication necessary for: a) data shuffling as a function of storage and topology; and b) the minimum time for computation as a function of intermediate communication and storage.