Advancements in biomedical research have driven continuous innovations in sensing and diagnostic technologies. Among these, nanopore based single molecule sensing and sequencing is rapidly emerging as a powerful and versatile sensing methodology. Advancements in nanopore based approaches require concomitant improvements in the electronic readout methods employed, from the point of low noise, bandwidth and form factor. This article focuses on current sensing circuits designed and employed for ultra low noise nanopore signal readout, addressing the fundamental limitations of traditional off chip transimpedance amplifiers (TIAs), which suffer from high input parasitic capacitance, bandwidth constraints, and increased noise at high frequencies. This review explores the latest design schemes and circuit structures classified into on-chip and off-chip TIA designs, highlighting their design implementation, performance, respective challenges and explores the interplay between noise performance, capacitance, and bandwidth across diverse transimpedance amplifier (TIA) configurations. Emphasis is placed on characterizing noise response under varying parasitic capacitance and operational frequencies, a systematic evaluation not extensively addressed in prior literature while also considering the allowable input current compliance range limitations. The review also compares the widely used Axopatch 200B system to the designs reported in literature. The findings offer valuable insights into optimizing TIA designs for enhanced signal integrity in high speed and high sensitivity applications focusing on noise reduction, impedance matching, DC blocking, and offset cancellation techniques.