Laser machining being a non-contact process possesses several advantages such as no tool wear or damage and no contact force induced problems. Laser cutting involves thermal process and it does not depend on the strength and hardness of the work piece, thus making it ideal for cutting non-homogeneous material. In this research work several papers related to the heat affected zone (HAZ) of laser machining of CFRP and GFRP are reviewed. It was found that laser parameters such as specific laser energy, laser power, repetition rate, work piece temperature determine the extent of HAZ. In CFRP HAZ in perpendicular laser grooving is much higher than that in parallel grooving. Presence of nitrogen jet decreases the work piece temperature leading to lower HAZ. Observations of the HAZ area of CFRP material revealed fiber swelling of 50 or 60% and fibers near the top are seen to curl up. In case of GFRP charred black material called shell and melted glass fibers are observed in the HAZ. It is also observed that the extent of HAZ affect the static tensile and bending strengths of CFRP. Tensile strength reduces linearly as HAZ increases. A comparison of laser cutting on CFRP using three types of laser is also presented here. Nd:YAG laser cutting on CFRP at optimized parameters has produced least HAZ and highest bending strength.