Wireless sensing of electrophysiological signals in day-to-day life will enable various clinical, research, and wellness applications. This paper reviews the design requirements of biosignal recording interfaces for use in remote, unconstrained environments and put the performance achieved by state-of-theart designs in perspective.In particular, we emphasize the need for biosignal recording front-ends to provide a dynamic range of approximately 100 dB, while meeting an input-referred noise level of a few µV rms. It is difficult to achieve a low input-referred noise and a high dynamic range using conventional voltage-domain amplifiers; state-of-theart designs provide only ∼60 dB of dynamic range. We propose to process electrophysiological signals in the phase domain, since there is no physical bound on phase. Low-noise VCO-based front-ends can be designed to extend the dynamic range by ∼40dB without paying a significant power, noise, or area penalty compared to state-of-the-art biosignal recording front-ends.For high-channel-count action-potential recording systems the system power is dominated by the transmitter if raw data is transmitted. In spite of the power reduction achieved by innovative biomedical transmitter designs, on-chip processing becomes necessary to reduce the output data rate for manychannel recording systems. It is important for neuroscientists and electrical engineers to agree upon a scheme to reduce the output data rate. We enlist and discuss a few data-rate reduction options for action-potential recordings. In addition, it is also desirable to make the biosignal sensors self-powered, thus avoiding the need for battery replacement/recharging. We briefly review existing energy-harvesting techniques and discuss future directions.