Spoken language recognition refers to the automatic process through which we determine or verify the identity of the language spoken in a speech sample. We study a computational framework that allows such a decision to be made in a quantitative manner. In recent decades, we have made tremendous progress in spoken language recognition, which benefited from technological breakthroughs in related areas, such as signal processing, pattern recognition, cognitive science, and machine learning. In this paper, we attempt to provide an introductory tutorial on the fundamentals of the theory and the state-of-the-art solutions, from both phonological and computational aspects. We also give a comprehensive review of current trends and future research directions using the language recognition evaluation (LRE) formulated by the National Institute of Standards and Technology (NIST) as the case studies.