This multidisciplinary research work aims to investigate the optimized information extraction from signals or data volumes and to develop tailored hardware implementations that trade-off the complexity of data acquisition with that of data processing, conceptually allowing radically new device designs. The mathematical results in classical Compressive Sampling (CS) support the paradigm of Analog-to-Information Conversion (AIC) as a replacement for conventional ADC technologies. The AICs simultaneously perform data acquisition and compression, seeking to directly sample signals for achieving specific tasks as opposed to acquiring a full signal only at the Nyquist rate to throw most of it away via compression. Our contention is that in order for CS to live up its name, both theory and practice must leverage concepts from learning. This work demonstrates our contention in hardware prototypes, with key trade-offs, for two different fields of application as edge and big-data computing. In the framework of edge-data computing, such as wearable and implantable ecosystems, the power budget is defined by the battery capacity, which generally limits the device performance and usability. This is more evident in very challenging field, such as medical monitoring, where high performance requirements are necessary for the device to process the information with high accuracy. Furthermore, in applications like implantable medical monitoring, the system performances have to merge the small area as well as the low-power requirements, in order to facilitate the implant bio-compatibility, avoiding the rejection from the human body. Based on our new mathematical foundations, we built different prototypes to get a neural signal acquisition chip that not only rigorously trades off its area, energy consumption, and the quality of its signal output, but also significantly outperforms the state-of-the-art in all aspects. In the framework of big-data and high-performance computation, such as in high-end servers application, the RF circuits meant to transmit data from chip-to-chip or chip-to-memory are defined by low power requirements, since the heat generated by the integrated circuits is partially distributed by the chip package. Hence, the overall system power budget is defined by its affordable cooling capacity. For this reason, application specific architectures and innovative techniques are used for low-power implementation. In this work, we have developed a single-ended multi-lane receiver for high speed I/O link in servers application. The receiver operates at 7 Gbps by learning inter-symbol interference and electromagnetic coupling noise in chip-to-chip communication systems. A learning-based approach allows a versatile receiver circuit which not only copes with large channel attenuation but also implements novel crosstalk reduction techniques, to allow single-ended multiple lines transmission, without sacrificing its overall bandwidth for a given area within the interconnect's data-path.