Childhood and adolescent obesity is a serious health problem that is on the rise at the global level. Earlier, certain diseases such as Type 2 diabetes, high blood pressure, and heart disease affected only adults, but now they are being detected in young children as well. Several studies based on machine learning have been proposed to develop obesity prediction models or to determine key determinants of obesity for designing intervention tools. Despite having a rich and diverse set of literature on obesity prediction models, obesity rates are at an all-time high for both children and adolescents. There is a need of proper understanding and critical analysis of existing machine learning models in order to design effective strategies for curbing obesity at childhood and adolescent level. This paper surveys the growing body of recent literature on machine and deep learning models for obesity prediction by providing a coherent view (critical analysis) of the limitations of the existing systems. The taxonomy of the existing literature on obesity prediction into methods used, predicted outcome, factors used, type of datasets, and the associated purpose, is discussed for analysis of the state-of-the-art. This analysis revealed that a) prediction-focused models do not use variables from as many domains as predictor-focused models do, b) very few studies proposed gender-specific and race-specific obesity prediction models, c) lack of large-scale multimodal datasets and d) existing predictor-focused models obtain an accuracy range of [53.7%, 96%] with an optimum set of predictors. Further, computer vision-based methods for obesity prediction and interpretable techniques for understanding the outcome of the models are discussed as well. In addition, we have also identified novel research directions. The overall aim is to advance the state-of-the-art and improve the quality of discourse in this field