Laser beam welding is the most modern and promising process for the automatic or robotized welding of structures of the highest Execution Class, EXC3-4, which are made of a variety of weldable structural materials, mainly steel, titanium, and nickel alloys, but also a limited range of aluminum, magnesium, and copper alloys, reactive materials, and even thermoplastics. This paper presents a systematic review and analysis of the author’s research results, research articles, industrial catalogs, technical notes, etc., regarding laser beam welding (LBW) and laser hybrid welding (LHW) processes. Examples of industrial applications of the melt-in-mode and keyhole-mode laser welding techniques for low-alloy and high-alloy steel joints are analyzed. The influence of basic LBW and LHW parameters on the quality of welded joints proves that the laser beam power, welding speed, and Gas Metal Arc (GMA) welding current firmly decide the quality of welded joints. A brief review of the artificial intelligence (AI)-supported online quality-monitoring systems for LBW and LHW processes indicates the decisive influence on the quality control of welded joints.