Naturalistic reading corpora are collections of texts that were not designed to be used in specific linguistic studies and that were read by participants whose eye-movements or reading time was measured. These resources are used to study the cognitive processing of linguistic phenomena naturally present in texts and they encourage the development of robust models of cognitive linguistic processing. These properties make the use of natural text corpora interesting for the study of pronoun and coreference resolution. In the psycholinguistic literature, many linguistic factors that have an influence on pronoun and coreference resolution have been identified but there is still a lot unknown about the interaction of these factors in naturalistic data. In addition, items used in psycholinguistic studies are short; therefore, naturalistic reading corpora are a resource to study pronoun and coreference resolution in realistic discourse. In this survey, we discuss the models for pronoun and coreference resolution that have been developed so far. We explain the methodological challenges related to the use of naturalistic data and speculate how such data can be used to evaluate theories of pronoun and coreference resolution and so lead to the development of broad coverage models in which various linguistic levels (syntax, semantics and discourse) are integrated.