Context: User intent modeling is a crucial process in Natural Language Processing that aims to identify the underlying purpose behind a user's request, enabling personalized responses. With a vast array of approaches introduced in the literature (over 13,000 papers in the last decade), understanding the related concepts and commonly used models in AI-based systems is essential. Method: We conducted a systematic literature review to gather data on models typically employed in designing conversational recommender systems. From the collected data, we developed a decision model to assist researchers in selecting the most suitable models for their systems. Additionally, we performed two case studies to evaluate the effectiveness of our proposed decision model. Results: Our study analyzed 59 distinct models and identified 74 commonly used features. We provided insights into potential model combinations, trends in model selection, quality concerns, evaluation measures, and frequently used datasets for training and evaluating these models. Contribution: Our study contributes practical insights and a comprehensive understanding of user intent modeling, empowering the development of more effective and personalized conversational recommender systems. With the Conversational Recommender System, researchers can perform a more systematic and efficient assessment of fitting intent modeling frameworks.