Recently, laser process modeling has gained widespread adoption, primarily due to its cost reduction and timesaving benefits, resulting in enhanced process efficiency and economically viable outcomes. Among various subsets of laser modeling processes, laser wobble welding modeling aims to overcome limitations inherent in traditional laser welding. Despite its evident advantages and numerous applications, research in this field is limited, lacking comprehensive studies or review papers. This study aims to bridge this gap by providing a contemporary assessment of the state of the art in simulating laser wobble welding, offering an in-depth analysis of the procedure. The study explores the heating and solidification modes within the laser wobble welding process, presenting various modeling methods through several case studies, encompassing analytical, numerical, and empirical approaches in the heating mode, along with a brief overview of select investigations in the solidification mode. Through meticulous examination of previous research, the study identifies gaps and trends in laser wobble welding modeling, with a particular emphasis on the solidification mode, categorizing these gaps and trends into modes, methods, error analysis, types of materials, and practical software. In conclusion, this study significantly contributes to the understanding of laser wobble welding modeling by furnishing a comprehensive overview of the current state of the field, addressing existing gaps, and delineating trends for future research and development.