Trajectory prediction is an important task to support safe and intelligent behaviours in autonomous systems. Many advanced approaches have been proposed over the years with improved spatial and temporal feature extraction. However, human behaviour is naturally multimodal and uncertain: given the past trajectory and surrounding environment information, an agent can have multiple plausible trajectories in the future. To tackle this problem, an essential task named multimodal trajectory prediction (MTP) has recently been studied, which aims to generate a diverse, acceptable and explainable distribution of future predictions for each agent. In this paper, we present the first survey for MTP with our unique taxonomies and comprehensive analysis of frameworks, datasets and evaluation metrics. In addition, we discuss multiple future directions that can help researchers develop novel multimodal trajectory prediction systems.