Alumina is one of the most commonly used engineering ceramics for a variety of applications ranging from microelectronics to prosthetics due to its desirable properties. Unfortunately, conventional machining techniques generally lead to fracture, tool failure, low surface integrity, high energy consumption, low material removal rate, and high tool wear during machining due to high hardness and brittleness of the ceramic material. Laser machining offers an alternative for rapid processing of brittle and hard engineering ceramics. However, the material properties, especially the high thermal expansion coefficient and low thermal conductivity, may cause ceramic fracture due to thermal damage. Striation formation is another defect in laser cutting. These drawbacks limit advanced ceramics in engineering applications. In this work, various lasers and machining techniques are investigated to explore the feasibility of high-quality laser machining different thicknesses of alumina. The main contributions include: (i) Fibre laser crack-free cutting of thick-section alumina (up to 6-mm-thickness). A three-dimensional numerical model considering the material removal was developed to study the effects of process parameters on temperature, thermal-stress distribution, fracture initiation and propagation in laser cutting. A rapid parameters optimisation procedure for crack-free cutting of thick-section ceramics was proposed. (ii) Low power CW CO2 laser underwater machining of closed cavities (up to 2-mm depth) in alumina was demonstrated with high-quality in terms of surface finish and integrity. A three-dimensional thermal-stress model and a two-dimensional fluid smooth particle hydrodynamic model (SPH) were developed to investigate the physical processes during CO2 laser underwater machining. SPH modelling has been applied for the first time to studying laser processing of ceramics. (iii) Striation-free cutting of alumina sheets (1-mm thickness) is realised using a nano-second pulsed DPSS Nd: YAG laser, which demonstrates the capability of high average power short pulsed lasers in high-quality macro-machining. A mechanism of pulsed laser striation-free cutting was also proposed. The present work opens up new opportunities for applying lasers for high-quality machining of engineering ceramics.