A context-aware system always needs to adapt its behaviors according to context changes; therefore, modeling context-aware requirements is a complex task. With the increasing use of mobile computing, research on methods of modeling context-aware requirements have become increasingly important, and a large number of relevant studies have been conducted. However, no comprehensive analysis of the challenges and achievements has been performed. The methodology of systematic literature review was used in this survey, in which 68 reports were selected as primary studies. The challenges and methods to confront these challenges in context-aware requirement modeling are summarized. The main contributions of this work are: (1) four challenges and nine sub-challenges are identified; (2) eight kinds of methods in three categories are identified to address these challenges; (3) the extent to which these challenges have been solved is evaluated; and (4) directions for future research are elaborated.