Purpose: This paper aims to analyse whether and how different types of institutional investors influence shareholder proposal initiations, say-on-pay (SOP) votes and management compensation from a sustainability perspective. Design/methodology/approach: Based on the principal-agent theory, the authors conduct a structured literature review and evaluate 40 empirical-quantitative studies on that topic. Findings: The traditional assumption of homogeneity within institutional investors, which is in line with the principal–agent theory, has to be questioned. Only special types of investors (e.g. with long-term and non-financial orientations and active institutions) run an intensive monitoring strategy, and thus initiate shareholder proposals, discipline managers by higher SOP dissents and prevent excessive management compensation. Research limitations/implications: A detailed analysis of institutional investor types is needed in future empirical analyses. In view of the current debate on climate change policy, future research could analyse in more detail the impact of institutional investor types on proxy voting, SOP and (sustainable) management compensation. Practical implications: With regard to the increased shareholder activism and regulations on SOP and management compensation since the 2007/2008 financial crisis, firms should be aware of the monitoring role of institutional investors and should analyse their specific ownership nature (time- and content-driven and as well as range of activity). Originality/value: To the best of authors’ knowledge, this is the first literature review with a clear focus on institutional investor range and nature, shareholder proposal initiation, SOP and management compensation (reporting) from a sustainability viewpoint. The authors explain the main variables that have been included in research, stress the limitations of this work and offer useful recommendations for future research studies.