Data and information fusion (DIF) involves a process of combining data and information from multiple inputs. The purpose is to derive enriched information compared to that obtained from each individual input. DIF techniques were first introduced to the research community in the 1970s. The scope of applications that use DIF techniques for problem-solving has extended tremendously from the military arena at the initial stage to many non-military sectors at present. The Joint Directors of Laboratories data fusion (JDL DF) model is possibly the most widely used model for data fusion. In this functional model, the hierarchical process of data and information fusion comprises two stages, the low-level fusion processes and the high-level fusion processes. After years of intensive research that is mainly focused on low-level information fusion (IF), the focus is currently shifting towards high-level information fusion. Compared to the increasingly mature field of low-level IF, theoretical and practical challenges posed by high-level IF are more difficult to handle. Contributing factors include the lack of: well-defined spatiotemporal constraints on relevant evidence, well-defined ontological constraints on relevant evidence and suitable models for causality. In this survey paper, we first review process models proposed for data and information fusion over the past few decades. Next, we present an overview of existing work on high-level information fusion, based on the fusion levels of the current JDL DF model. Finally, we discuss relevant application areas and topics with potential for further research.