Quantum cognition research applies abstract, mathematical principles of quantum theory to inquiries in cognitive science. It differs fundamentally from alternative speculations about quantum brain processes. This topic presents new developments within this research program. In the introduction to this topic, we try to answer three questions: Why apply quantum concepts to human cognition? How is quantum cognitive modeling different from traditional cognitive modeling? What cognitive processes have been modeled using a quantum account? In addition, a brief introduction to quantum probability theory and a concrete example is provided to illustrate how a quantum cognitive model can be developed to explain paradoxical empirical findings in psychological literature.Keywords: Quantum probability; Classical probability; Cognitive process; Compatibility; Entanglement; Non-Boolean logic With astonishing counterintuitive ramifications, quantum theory is the best empirically confirmed scientific theory in human history. It is "essential to every natural science" and its practical applications, such as the laser and the transistor, form the direct basis of at least one-third of our current economy (Rosenblum & Kuttner, 2006, p. 81). However, applying quantum theory to human cognition is not merely a simple extension of a most successful scientific theory. Rather, this endeavor is driven by a myriad of puzzling findings and stubborn challenges in psychological literature, by deep resonations between basic notions of quantum theory and psychological conceptions and intuitions, and by the Correspondence should be sent to Zheng Wang, School of Communication, The Ohio State University, 3045 Derby Hall, 154 N Oval Mall, Columbus OH 43210-1339 exhibited potential of the theory to provide coherent and mathematically principled explanations for the puzzles and challenges in human cognitive research (Busemeyer & Bruza, 2012).Given the still nascent status of quantum cognition research, it is important to note that it differs from the approaches which treat (parts of) the brain literally as material quantum systems or a quantum computer (e.g., Beck & Eccles, 1992;Hameroff & Penrose, 1996; Stapp, 1993;Vitiello, 1995). In contrast, our approach applies abstract, mathematical principles of quantum theory to inquiries in cognitive science. In fact, to convey the idea that researchers in this area are not doing quantum mechanics, various modifiers have been proposed to describe the approach, such as cognitive models based on quantum structure (Aerts, 2009), quantum-like models (Khrennikov, 2010), and generalized quantum models (Atmanspacher, R€ omer, & Walach, 2002).This topic presents new developments within the quantum cognition modeling research program. In the introduction to this special issue, we try to answer three questions: Why apply quantum concepts to human cognition? How is quantum cognitive modeling different from traditional cognitive modeling? What cognitive processes have been modeled using a quantum account? In addi...