The presentation starts by demonstrating in a descriptive way the origin of information theory in Shannon's 1948 monumental work, and pointing some interdisciplinary aspects within general areas of electrical engineering and beyond. We discuss a change of paradigms in information theory from being a pure mathematical theory of communications to a theory with widescope direct practical implications and applications. To demonstrate the rich aspects of the problems considered and their implications as well as some inter-disciplinary connections, we focus on a simple matrix based linear additive Gaussian model. We elaborate on the information-estimation intimate connection, mentioning its impact on non-linear filtering and on recent views of efficient coding in single and multi-terminal channels. Possible  extensions and a short outlook conclude the presentation