Carbon fibre-reinforced polymer (CFRP) composite materials are in increasingly high demand, particularly in aerospace and automotive industries for reduced fuel consumption. This is due to their superior structural characteristics (both in fatigue and static conditions) and light weight. Anisotropic and heterogeneous features of these materials, however, have posed serious challenges in machining of CFRPs. Hence new machining technologies need to be investigated. Laser is a non-contact (eliminating toolwear) thermal process. Therefore, the thermal properties of the material are of crucial importance. Especially for composite materials which consist of different constituent materials. In CFRPs, carbon fibres are excellent conductors of heat (thermal conductivity of 50 W/(m.K)) while the polymer matrix is poor conductor (thermal conductivity of 0.1-0.3 W/(m.K)). This significant difference that can be similarly traced for other thermal properties such as heat of vaporisation and specific heat capacity are the source of defects in laser cutting of CFRP composites. Major quality challenges in laser cutting of these materials are delamination and matrix recession. Various laser systems and cutting techniques are investigated in this work to minimise these defects. Multiple-pass cutting using a high beam quality continuous wave (CW) mode fibre laser is found to be effective to minimise delamination at low power level and high scanning speeds. Multiple-pass cutting using nanosecond pulsed DPSS Nd:YAG laser is shown to reduce matrix recession. A novel technique using mixing of reactive and inert gases is introduced and demonstrated to minimise the matrix recession. In order to improve the quality and dimensional accuracy of CFRP laser machining, it is important to understand the mechanism of transient thermal behaviour and its effect on material removal. A three-dimensional model to simulate the transient temperature field and subsequent material removal is developed, for the first time, on a heterogeneous fibre-matrix mesh. In addition to the transient temperature field, the model also predicts the dimensions of the matrix recession during the laser machining process.