Supercritical fluids (SCFs) offer promising potential for creating efficient, compact, and sustainable energy systems due to their ability to enhance heat transfer and enable more efficient power cycles. However, SCFs exhibit complex behaviors near their critical points, where small variations in temperature and pressure can lead to flow instability. Understanding and mitigating flow instability in SCFs is crucial for ensuring the safe and reliable operation of advanced energy systems. In this systematic review the research questions were formulated to identify the influencing factors, their effect, and strategies to tackle the SCFs flow instability. Although research on SCFs flow instability is limited, the review revealed that following influencing factors were investigated by researchers: flow direction, geometric parameters, inlet orifice coefficient, heat flux, mass flow rate, inlet temperature and pressure. These factors have significant effects on the SCFs flow instability which are summarized in detailed in the article. Additionally, this review discusses flow instability mitigation strategies, and associated challenges. The insights from this review highlight the needs for ongoing research and innovative approaches to enhance the safety of SCFs applications, paving the way for advancements in next-generation technologies.