For an Operational Transconductance Amplifier- Capacitor (OTA-C) integrated circuit implementation, this directly translates to a very small transconductance (of the order of a few nA/V) and a very large on-chip capacitance (of the order of several hundred pF). Both the above mentioned aspects of low frequency IC design are addressed in this work. Specifically, a family of OTA' s with very small transconductance has been designed using several design schemes such as current division, use of floating gate MOS and bulk driven transistors. A detailed comparison has been made among these schemes in terms of performance characteristics such as power consumption, active silicon area and signal to noise ratio. A multiplier based OTA with very small transconductance has also been designed with a view to obtain a wide transconductance tuning range. Moreover, an impedance scaling circuit has also been designed in order to realize very large capacitors on-chip. As sample applications for these circuits, a low pass filter, relaxation oscillator, band pass filter and a band pass based oscillator have also been designed, fabricated in a 1.2um analog process and successfully tested in the lab.