Cloud computing offers a promising approach to efficiently distribute tasks and workflows among virtual resources. Optimal scheduling of these resources is crucial to maximize the efficiency of cloud environments. Various nature-inspired metaheuristic solutions have been suggested to tackle this challenge, focusing on Genetic Algorithm (GA)-based techniques. GA has the capability to effectively manage the intricate and ever-changing characteristics of cloud task scheduling, hence enhancing the allocation of resources in accordance with present requirements. In this study, we comprehensively analyze GA-based techniques for cloud task scheduling by performing a Systematic Literature Review (SLR). Our review involves selecting relevant studies from online electronic databases based on predefined research questions (RQs) and criteria. We narrowed the selection from 385 articles to a final set of 20 articles that provide valuable insights into our research inquiries and form the foundation of our analysis. We explore different aspects of the literature, such as its properties, benefits, drawbacks, datasets, simulation tools, performance evaluations, and function objectives. Based on this analysis, we propose a classification framework incorporating a modified and hybrid GA method for scheduling tasks and workflows. Furthermore, we outline future research directions in this field. The overall efficacy of GA-modified and GA-Hybrid algorithms is very commendable. However, it is crucial to consider the intricacy and the potential for being confined to local optima in order to get more optimal outcomes in task scheduling.