Abstract: Owing to their exceptional combination of properties including low density, intrinsic light weight, high specific strength and hardness, and outstanding corrosion resistance, aluminum alloys have become core structural materials in critical sectors such as aerospace, automotive manufacturing, electronics, and telecommunications. The emergence of additive manufacturing (AM), particularly laser powder bed fusion (LPBF) technology, has revolutionarily transformed the design and manufacture of geometrically complex aluminum alloy components. These components are often difficult or impossible to produce using conventional manufacturing methods. As a core laser-based AM technology, LPBF uses a high-energy laser beam to selectively melt and fuse fine metallic powder layers within a precisely controlled atmosphere, enabling the layer-by-layer fabrication of intricate near-net-shape parts. This capability places LPBF at the forefront of cutting-edge AM research and industrial applications for high-value aluminum alloy parts. This review systematically synthesizes and analyzes the significant research progress achieved in the LPBF processing of aluminum alloys. It outlines the fundamental physical principles of the LPBF process and elucidates its unique advantages over traditional subtractive or formative manufacturing techniques (such as casting and forging), including unparalleled design freedom, minimal material waste, and the potential for rapid prototyping and customized production. This review candidly identifies the major challenges currently hindering the broader adoption of LPBF for aluminum alloys. These challenges include the persistently narrow LPBF processing window, difficulties in controlling metallurgical defects, the contradiction between simultaneous enhancement of strength and ductility (strength–ductility trade-off), pronounced sensitivity associated with columnar-grain-dominated solidification microstructures, significant hurdles in engineering application scale-up, and limitations in the existing alloy systems specifically optimized for the rapid solidification characteristics inherent to LPBF. Furthermore, this review provides a comprehensive overview of the current research status of several industrially crucial wrought aluminum alloy systems processed via LPBF. These primarily include Al–Cu (2xxx series), Al–Si (4xxx series), Al–Mg (5xxx series), and ultrahigh-strength Al–Zn–Mg–Cu (7xxx series) alloys. Focusing on the key challenges in LPBF processing across different alloy systems—particularly the high hot-cracking susceptibility of Al–Cu and Al–Zn–Mg–Cu alloys, the strength–ductility trade-off in Al–Si alloys, and the need for enhanced strength–toughness synergy in Al–Mg alloys—this review provides an in-depth discussion of hot-cracking formation mechanisms. It systematically outlines the current strategies for defect suppression and microstructure optimization through alloy composition design and process parameter regulation. Furthermore, the critical role of post-heat treatments in tailoring precipitate characteristics and improving the overall mechanical performance is examined. Finally, this review rigorously examines the core scientific and technological problems persisting within the current LPBF aluminum alloy technology. Building on this critical analysis, it proposes forward-looking perspectives for future research. The ultimate objective is to provide robust scientific insights and theoretical underpinnings to guide the development of next-generation LPBF-dedicated aluminum alloys. These alloys are expected to significantly reduce hot-cracking susceptibility while simultaneously achieving an optimized combination of high strength, high toughness, superior fatigue performance, and excellent corrosion resistance, thereby fully unlocking the potential of LPBF technology for demanding structural applications.