There are many varieties of systematic reviews - a typology of systematic reviews may be helpful in determining the type of review best suited to your research. Additional tools to help you determine which is the right review for you include Cornell University's Systematic Review decision tree, and the Right Review tool.
Some commonly found types of systematic reviews beyond the standard approach include:
Rapid Reviews - a streamlined approach to a systematic review within time constraints. Rapid reviews use methods to accelerate or streamline traditional systematic review processes, and are commonly used by government policymakers, healthcare institutions, health professionals, and patient associations to inform health system planning and policy development. (Ganann, R., Ciliska, D. & Thomas, H., 2010).
Ganann, R., Ciliska, D., & Thomas, H. (2010). Expediting systematic reviews: Methods and implications of rapid reviews. Implementation Science, 5(1), 56-56. doi:10.1186/1748-5908-5-56
Scoping Reviews - these differ from classic systematic reviews in a number of ways. Arksey and O'Malley (2005) describe a classic systematic review as a deeper exploration of a more well-defined question using identified study designs, while a scoping review will consider broader topics of inquiry where many different study designs may be applicable. They further define the goals of a scoping review as the following:
Arksey, H., & O'Malley, L. (2005). Scoping studies: Towards a methodological framework. International Journal of Social Research Methodology, 8(1), 19-32. doi:10.1080/1364557032000119616
Meta-Analysis - Glass (1976) describes a meta-analysis as "the statistical analysis of a large collection of analysis results from individual studies for the purpose of integrating the findings" (p. 3). As a result, the application of this technique can provide an overall measure of the effect of one treatment or intervention over another. The researcher or research team must determine if sufficient homogeneity exists in the results to justify pursuing a meta-analysis. A good explanation of the steps to consider when conducting a meta-analysis is described by Blundell (2014) in Ch. 6 of Doing a Systematic Review: A Student's Guide.
Boland, A., Cherry, M. G., & Dickson, R. (2014). Doing a systematic review: A student's guide. SAGE.
Glass, G. (1976). Primary, Secondary, and Meta-Analysis of Research. Educational Researcher, 5(10), 3-8. doi:10.2307/1174772