Manufacturing businesses aiming to deliver their new customised products more quickly and gain more consumer markets for their products will increasingly employ selective laser sintering/melting (SLS/SLM) for fabricating high quality, low cost, repeatable, and reliable aluminium alloy powdered parts for automotive, aerospace, and aircraft applications. However, aluminium powder is known to be uniquely bedevilled with the tenacious surface oxide film which is difficult to avoid during SLS/SLM processing. The tenacity of the surface oxide film inhibits metallurgical bonding across the layers during SLS/SLM processing and this consequently leads to initiation of spheroidisation by Marangoni convection. Due to the paucity of publications on SLS/SLM processing of aluminium alloy powders, we review the current state of research and progress from different perspectives of the SLS/SLM, powder metallurgy (P/M) sintering, and pulsed electric current sintering (PECS) of ferrous, non-ferrous alloys, and composite powders as well as laser welding of aluminium alloys in order to provide a basis for follow-on-research that leads to the development of high productivity, SLS/SLM processing of aluminium alloy powders. Moreover, both P/M sintering and PECS of aluminium alloys are evaluated and related to the SLS process with a view to gaining useful insights especially in the aspects of liquid phase sintering (LPS) of aluminium alloys; application of LPS to SLS process; alloying effect in disrupting the surface oxide film of aluminium alloys; and designing of aluminium alloy suitable for the SLS/SLM process. Thereafter, SLS/SLM parameters, powder properties, and different types of lasers with their effects on the processing and densification of aluminium alloys are considered. The microstructure and metallurgical defects associated with SLS/SLM processed parts are also elucidated by highlighting the mechanism of their formation, the main influencing factors, and the remedial measures. Mechanical properties such as hardness, tensile, and fatigue strength of SLS/SLM processed parts are reported. The final part of this paper summarises findings from this review and outlines the trend for future research in the SLS/SLM processing of aluminium alloy powders.