From the "Rayleigh quotients" used in 19th century Sturm-Liouville theory to the present-day applications in QIT (quantum information theory), the study of numerical ranges and numerical radii has a long and distinguished history. Currently, a great deal of active research is conducted by different research groups around the world. A subject search on "numerical range" alone using MathSciNet will return over 1000 items. Many recent Ph.D. theses have been devoted entirely or in part to this subject. There are monographs, special issues of research journals, and chapters of textbooks devoted to the subject. Research papers on the subject continually appear in mathematical journals. Talks on the subject are frequently presented in mathematical conferences. In short, the importance of this subject area in current mathematical research is undeniable. A principal reason for this high level of activity lies in its relation and applicability to many different branches of pure and applied science, including operator theory, functional analysis C*-algebras, Banach algebras, indefinite inner product spaces, matrix norms and inequalities, numerical analysis, perturbation theory, matrix polynomials, multilinear algebra, systems theory, and quantum information science. Moreover, a wide range of mathematical tools including algebra, analysis, geometry, combinatorial theory, and computer programming come into play in this study. In the early seventies, highly influential numerical range workshops were organized by Bonsall and Duncan. A modern series of workshops on the subject was initiated in 1992 at Williamsburg. These became widely known by the acronym WONRA (Workshop on Numerical Ranges and Applications). After 1992 the workshops were held biennially in different countries: at Coimbra, Portugal in 1994; at Sapporo, Japan in 1996; at Madison, USA in 1998; at Napflio, Greece in 2000; at Auburn, USA in 2002; at Coimbra, Portugal in 2004; at Bremen, Germany in 2006; at Williamsburg, USA in 2008; at Krakow, Poland in 2010; and most recently at Kaohsiung, Taiwan in 2012. We are pleased to hold WONRA2014 at Sanya.