This study explores the core values, purposes, functions, and objectives of libraries. Based on the library values identified in the existing literature, this study conducted empirical analyses and proposed a set of core competencies for librarians in Taiwan. Firstly, focus group method was used to understand librarians’ opinions on the subject matter. Two documents released by the American Library Association informed the discussion protocols--the 2004 Core Values of Librarianship as well as the 2008 Core Competencies of Librarianship. Secondly, based on the results of three focus group discussions, a questionnaire surveying librarians’ opinions of library values and core competencies for Taiwan’s librarians was distributed to library managers and library educators. Based on the survey result, this study identified 12 library values, 11 librarian roles, and a set of core competencies comprised of 55 items in eight categories. It also identified 14 new library functions in the digital age. The findings can be used in the planning of library education and the hiring and evaluation of library employees.