Infinite impulse response (IIR) is a property applying to many linear time-invariant systems. Digital filters are the common example of linear time invariant systems. Systems with this property are called IIR systems or IIR filters. These filters have infinite length of impulse response and are in contrast to finite impulse response (FIR) filters. The basic IIR filters are – Butterworth filters, Chebyshev filters and Elliptic filters. In this paper we are going to discuss some basic theory of these filters and then we will analyze the properties of these filters.