As is well known, some students are more successful than others in language learning. This different level of achievement may be attributed to variables associated with the teachers and students. In recent years there has been extensive research into aspects of differences in learning a second language. Some dimensions of learner differences are generally acknowledged such as age, aptitude, motivation, cognitive style, anxiety, attitude and learning strategies. In my paper I attempt to review and discuss one of them — anxiety — which research studies indicate may influence students' achievements of language learning.