Context: Over the last decade, software researchers and engineers have developed a vast body of methodologies and technologies in requirements engineering for self-adaptive systems. Although existing studies have explored various aspects of this field, no systematic study has been performed on summarizing modeling methods and corresponding requirements activities. Objective: This study summarizes the state-of-the-art research trends, details the modeling methods and corresponding requirements activities, identifies relevant quality attributes and application domains and assesses the quality of each study. Method: We perform a systematic literature review underpinned by a rigorously established and reviewed protocol. To ensure the quality of the study, we choose 21 highly regarded publication venues and 8 popular digital libraries. In addition, we apply text mining to derive search strings and use Kappa coefficient to mitigate disagreements of researchers. Results: We selected 109 papers during the period of 2003-2013 and presented the research distributions over various kinds of factors. We extracted 29 modeling methods which are classified into 8 categories and identified 14 requirements activities which are classified into 4 requirements timelines. We captured 8 concerned software quality attributes based on the ISO 9126 standard and 12 application domains. Conclusion: The frequency of application of modeling methods varies greatly. Enterprise models were more widely used while behavior models were more rigorously evaluated. Requirements-driven runtime adaptation was the most frequently studied requirements activity. Activities at runtime were conveyed with more details. Finally, we draw other conclusions by discussing how well modeling dimensions were considered in these modeling methods and how well assurance dimensions were conveyed in requirements activities.