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Natural language processing (NLP) is as yet far from achieving human levels of sophistication. This isn't surprising if we consider that people are amazing processors of language who leverage all of their knowledge of language, the speech context and the world in every language situation. A domain in which the divergence between the abilities of people and the abilities of machines is particularly manifest is reference resolution. Reference resolution is best defined as interpreting the meaning of each referring expression in a language input - like my finger, JFK, them, ran - and anchoring it in the mental model (memory) of the intelligent agent processing that input. This semantics-oriented, memory-oriented view of reference resolution is inspired by what people seem to accomplish when resolving reference. It stands in contrast to the more widely pursued NLP task of coreference resolution, whose final goal is to match coreferential text strings (words and phrases) with each other, typically with little or no connection to text meaning or memory population and management. This article provides an example-oriented overview of reference phenomena that are difficult for intelligent agents to process, as well as the types of knowledge, rendered machine tractable, that seem to be required to process them. We begin with a short introduction to "deep semantic" text processing, an approach to NLP that is currently not widely pursued but seems necessary to tackle problems like advanced reference resolution. Next comes an extended example that provides a concrete picture of the problem space in question. Then the full scope of reference phenomena is juxtaposed with the much narrower scope of phenomena that has been treated in systems to date. Comparisons are drawn between the primarily knowledge-lean approach, which has dominated the field so far, and the primarily knowledge-rich approach, which seems necessary for difficult phenomena. Following that are seven high-level qu- estions and their answers that highlight some key challenges faced by reference resolving agents. The article concludes with some thoughts about what to do next in order to make significant progress on reference resolution. The organizational style - example-driven and Q&A - was selected to provide a more engaging introduction to the topic than would a formal, linguistically motivated classification.