Error correcting codes are combinatorial objects which have traditionally been used to enhance the transmission of data on unreliable media. They have experienced a phenomenal growth since their birth some fifty years ago. Today, everyday tasks such as listening to a CD, accessing the hard disk of an electronic device, talking on a wireless phone, or downloading files from the Internet are impossible without the use of error-correcting codes. Though traditional communication still occupies centerstage in the realm of applied coding theory, emerging applications are changing the rules of the game, and calling for a new type of coding theory capable of addressing future needs. These are not limited to physical applications, however. In fact, coding theory is an integral part of solutions offered by researchers outside traditional physical communication to solve fundamental problems of interest, such as the complexity of computation, reliable transfer of bulk data, cryptographic protocols, self correcting software, signal processing, or even computational biology.While research in the past fifty years has put traditional coding theory on firm theoretical grounds, emerging applications are in need of new tools and methods to design, analyze, and implement coding technologies capable of dealing with future needs. This is the main concern of the present proposal. To strike the right balance between length and impact we have identified five areas of research that span the full spectrum of coding theory ranging from fundamental theoretical aspects to practical applications. We set out to develop new theoretical and practical models for the design and analysis of codes, and explore new application areas hitherto untouched. A unique feature of this proposal is our choice of the tools, ranging from classical areas of algebra, combinatorics, and probability theory, to ideas and methods from theoretical computer science.