Recent developments in deep learning have enabled data-driven algorithms that can reach human-level performance and beyond. The development and deployment of medical image analysis methods have several challenges, including data heterogeneity due to population diversity and different device manufacturers. In addition, more input from experts is required for a reliable method development process. While the exponential growth in clinical imaging data has enabled deep learning to flourish, data heterogeneity, multi-modality, and rare or inconspicuous disease cases still need to be explored. Endoscopy being highly operator-dependent with grim clinical outcomes in some disease cases, reliable and accurate automated system guidance can improve patient care. Most designed methods must be more generalisable to the unseen target data, patient population variability, and variable disease appearances. The paper reviews recent works on endoscopic image analysis with artificial intelligence (AI) and emphasises the current unmatched needs in this field. Finally, it outlines the future directions for clinically relevant complex AI solutions to improve patient outcomes.