Body weight measurement of animals is often labor-intensive for farmers and stressful for animals. To this end, several methods have been researched and implemented to automate this process. In this study, we performed a Systematic Literature Review to identify and synthesise the published studies on the body weight estimation approaches for livestock (i.e. cattle and pigs). Information about features of models, underlying methods, performance evaluation parameters, challenges, and solutions using computer vision-based weight estimation, and characteristics of the future vision-based weight estimation models were presented based on the identified scientific papers. We found 151 papers, of which 26 papers were selected as primary studies that we analyzed in detail. We identified that: (1) seven features, namely top view body area, withers height, hip height, body length, hip-width, body volume, and chest girth are widely used in approaches; (2) 3D Time of Flight camera is the most preferred one; (3) the linear regression is the most used algorithm; (4) the application of Deep Learning algorithms is still very limited; and (5) coefficient of determination is the most used evaluation parameter for weight estimation. In addition to these observations, 13 challenges, 22 solutions, and guidelines for future research direction were presented.