Biological signal sensing and processing has greatly improved our understanding about the body. With the increased number of high quality biosignals that can be sensed from the body, more efficient sensing and processing systems are detrimental to meet requirements of high bandwidth data measurement and processing in power and area limited settings. Power limitation is more and more stringent with the goal of making unobtrusive wearable/implantable devices, where the battery should be long-lasting (e.g., weeks) and as small as possible at the same time. A conventional wearable/implantable biological signal sensing system includes analog-front-end to measure a biosignal, analog-to-digital converter for conversion of the measured signal, and radio to transmit the digitized signal. The most power-hungry block among them is radio, where the power consumption increases with data bandwidth. To overcome the radio power domination, physiologically relevant information can be extracted on sensing system, which would significantly reduce the transferred data bandwidth. Notably, while achieving radio power savings, the accuracy of the on-chip processing should be high. To achieve ultra-low power and high accuracy on-chip processing in resource limiting settings, the dissertation presents two ways. The first path focuses on implementation of a high accuracy digital biological signal processing algorithm in the analog signal processing (ASP) domain. Presented ASP implementation of a high accuracy algorithm achieves high electrocardiogram (ECG) feature detection with the lowest power consumption reported. In the second path, a novel biosignal processing algorithm with physical roots is introduced for intracortical neural spike and ECG feature detection. Moreover, a physical implementation of the developed algorithm with physical computation elements is designed and validated against public and custom datasets. The algorithm with physical origins achieves better signal enhancement and feature detection than widely used ECG and intracortical neural signal enhancement algorithms. Additionally, its ultra-low power physical implementation offers real-time operation while not compromising accuracy. In the dissertation, first, algorithm-level discussions are presented, which are followed by circuit design discussions. Before going into details of algorithms, in Introduction, significance of real-time and accurate ultra-low power on-chip processing is emphasized.