Cancer is a life-threatening concern worldwide. Sensitive and early-stage diagnostics of different cancer types can make it possible for patients to get through the best available treatment options to combat this menace. Among several new detection methods, aptamer-based biosensors (aptasensors) have recently shown promising results in terms of sensitivity, identification, or detection of either cancerous cells or the associated biomarkers. In this mini-review, we have summarized the most recent (2016–2020) developments in different approaches belonging to optical aptasensor technologies being widely employed for their simple operation, sensitivity, and early cancer diagnostics. Finally, we shed some light on limitations, advantages, and current challenges of aptasensors in clinical diagnostics, and we elaborated on some future perspectives.