In recent years, considerable effort has been directed towards the synthesis of conjugated polymers with low optical band gaps (Eg), since they show intrinsic electrical conductivity. One of the approaches towards the designing of such polymers is the use of strong donor and acceptor monomers at regular arrangements in the repeating units, which has limited success in many cases. An alternate strategy is the use of organic dyes, having inherently low HUMO-LUMO separation, as building blocks. Extension of conjugation in organic dyes is therefore expected to result in oligomers and polymers with near infrared absorption, which is a signature of low band gaps. Squaraine dyes are ideal candidates for this purpose due to their unique optical properties. This review highlights the recent developments in the area of donor-acceptor type low band gap polymers with special emphasis on polysquaraines.