The past four decades have seen an increase in the incidence of early-onset gastrointestinal cancer. Because early-stage cancer detection is vital to reduce mortality rate, mass screening colonoscopy provides the most effective prevention strategy. However, conventional endoscopy is a painful and technically challenging procedure that requires sedation and experienced endoscopists to be performed. To overcome the current limitations, technological innovation is needed in colonoscopy. In recent years, researchers worldwide have worked to enhance the diagnostic and therapeutic capabilities of endoscopes. The new frontier of endoscopic interventions is represented by robotic flexible endoscopy. Among all options, self-propelling soft endoscopes are particularly promising thanks to their dexterity and adaptability to the curvilinear gastrointestinal anatomy. For these devices to replace the standard endoscopes, integration with embedded sensors and advanced surgical navigation technologies must be investigated. In this review, the progress in robotic endoscopy was divided into the fundamental areas of design, sensing, and imaging. The article offers an overview of the most promising advancements on these three topics since 2018. Continuum endoscopes, capsule endoscopes, and add-on endoscopic devices were included, with a focus on fluid-driven, tendon-driven, and magnetic actuation. Sensing methods employed for the shape and force estimation of flexible endoscopes were classified into model- and sensor-based approaches. Finally, some key contributions in molecular imaging technologies, artificial neural networks, and software algorithms are described. Open challenges are discussed to outline a path toward clinical practice for the next generation of endoscopic devices.