Word learning happens in everyday contexts with many words and many potential referents for those words in view at the same time. It is challenging for young learners to find the correct referent upon hearing an unknown word at the moment. This problem of referential uncertainty has been deemed as the crux of early word learning (Quine, 1960). Recent empirical and computational studies have found support for a statistical solution to the problem termed cross-situational learning. Cross-situational learning allows learners to acquire word meanings across multiple exposures, despite each individual exposure is referentially uncertain. Recent empirical research shows that infants, children and adults rely on cross-situational learning to learn new words (Smith & Yu, 2008; Suanda, Mugwanya, & Namy, 2014; Yu & Smith, 2007). However, researchers have found evidence supporting two very different theoretical accounts of learning mechanisms: Hypothesis Testing (Gleitman, Cassidy, Nappa, Papafragou, & Trueswell, 2005; Markman, 1992) and Associative Learning (Frank, Goodman, & Tenenbaum, 2009; Yu & Smith, 2007). Hypothesis Testing is generally characterized as a form of learning in which a coherent hypothesis regarding a specific word-object mapping is formed often in conceptually constrained ways. The hypothesis will then be either accepted or rejected with additional evidence. However, proponents of the Associative Learning framework often characterize learning as aggregating information over time through implicit associative mechanisms. A learner acquires the meaning of a word when the association between the word and the referent becomes relatively strong. In this chapter, we consider these two psychological theories in the context of cross-situational word-referent learning. By reviewing recent empirical and cognitive modeling studies, our goal is to deepen our understanding of the underlying word learning mechanisms by examining and comparing the two theoretical learning accounts.