[Context] Stream processing is a popular paradigm to continuously process huge amounts of data. Runtime adaptation plays a significant role in supporting the optimization of data processing tasks. In recent years runtime adaptation has received significant interest in scientific literature. However, so far no categorization of the enactment approaches for runtime adaptation in stream processing has been established. [Objective] This paper identifies and characterizes different approaches towards the enactment of runtime adaptation in stream processing with a main focus on latency as quality dimension. [Method] We performed a systematic literature review (SLR) targeting five main research questions. An automated search, resulting in 244 papers, was conducted. 75 papers published between 2006 and 2018 were finally included. From the selected papers, we extracted data like processing problems, adaptation goals, enactment approaches of adaptation, enactment techniques, evaluation metrics as well as evaluation parameters used to trigger the enactment of adaptation in their evaluation. [Results] We identified 17 different enactment approaches and categorized them into a taxonomy. For each, we extracted the underlying technique used to implement this enactment approach. Further, we identified 9 categories of processing problems, 6 adaptation goals, 9 evaluation metrics and 12 evaluation parameters according to the extracted data properties. [Conclusion] We observed that the research interest on enactment approaches to the adaptation of stream processing has significantly increased in recent years. The most commonly applied enactment approaches are parameter adaptation to tune parameters or settings of the processing, load balancing used to re-distribute workloads, and processing scaling to dynamically scale up and down the processing. In addition to latency, most adaptations also address resource fluctuation / bottleneck problems. For presenting a dynamic environment to evaluate enactment approaches, researchers often change input rates or processing workloads.