There are two main avenues along which classical Information Theory has progressed since 1948.
1) Bounds on Communication: Converse-to-coding theorems, the Data Processing theorem, Rate distortion theory, etc.
2) Coding theorems and algorithms: Theorems and algorithms that addresses the realization of these bounds, thus establishing their tightness and the optimality of the algorithms that are associated with the coding theorems.
Some of the classical results are asymptotic in nature and refer to cases where the "block-length" (or "constraint-length") tends to infinity. In practice, very long blocks result in causing a very large encoding and decoding delay and/or in yielding a large computational complexity.
For example, in the case of universal source coding, the classical results that establish the optimality of various universal coding theorems and algorithms are also asymptotic in nature (i.e. assuming that the amount of training data tends to infinity, or that the length of the input string to be compressed, tends to infinity).
It is therefore imperative to try to re-derive the classical results, converse theorems and coding theorems, under the assumption that parameters like delay, processor memory, and computational complexity are constrained.
Old and new results and attempts to address these problems, some more successful than others, will be critically discussed in this presentation.