This thesis presents experimental and computational modeling studies on the mental representations of the natural language quantifiers (e.g., most, many, few, more than half, and fewer than half). According to the dominant logical approach in cognitive semantics, the meaning of quantifiers can be expressed in the form of truth conditions. The thesis argues that the logical perspective on quantifiers is insufficient to capture psychological phenomena related to the processing of quantified sentences. The logical perspective thus should be extended to a cognitive perspective. The cognitive perspective considers both truth-conditional representations of quantifiers and individual differences in meaning representations. It also stresses the importance of computational modeling in experimental semantics. The thesis consists of seven chapters: Introduction, five chapters presenting experimental studies, and Conclusions. Chapters 2 and 3 of the thesis present experimental and modeling findings on individual differences in quantifier representations. Chapters 4 and 5 investigate the differences in the processing of positive (e.g., more than half) and negative (e.g., fewer than half) quantifiers in behavioral and electroencephalography experiments. Chapter 6 presents an experiment that tested the learnability explanation of semantic universals.