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Visualization and visual analysis play important roles in exploring, analyzing, and presenting scientific data. In many disciplines, data and model scenarios are becoming multifaceted: data are often spatiotemporal and multivariate; they stem from different data sources (multimodal data), from multiple simulation runs (multirun/ensemble data), or from multiphysics simulations of interacting phenomena (multimodel data resulting from coupled simulation models). Also, data can be of different dimensionality or structured on various types of grids that need to be related or fused in the visualization. This heterogeneity of data characteristics presents new opportunities as well as technical challenges for visualization research. Visualization and interaction techniques are thus often combined with computational analysis. In this survey, we study existing methods for visualization and interactive visual analysis of multifaceted scientific data. Based on a thorough literature review, a categorization of approaches is proposed. We cover a wide range of fields and discuss to which degree the different challenges are matched with existing solutions for visualization and visual analysis. This leads to conclusions with respect to promising research directions, for instance, to pursue new solutions for multirun and multimodel data as well as techniques that support a multitude of facets.