Background & Motivation: Biomedical image segmentation (BIS) task is challenging due to the variations in organ types, position, shape, size, scale, orientation, and image contrast. Conventional methods lack accurate and automated designs. Artificial intelligence (AI)-based UNet has recently dominated BIS. This is the first review of its kind that microscopically addressed UNet types by complexity, stratification of UNet by its components, addressing UNet in vascular vs. non-vascular framework, the key to segmentation challenge vs. UNet-based architecture, and finally interfacing the three facets of AI, the pruning, the explainable AI (XAI), and the AI-bias. Methods: PRISMA was used to select 267 UNet-based studies. Five classes were identified and labeled as conventional UNet, superior UNet, attention-channel UNet, hybrid UNet, and ensemble UNet. We discovered 81 variations of UNet by considering six kinds of components, namely encoder, decoder, skip connection, bridge network, loss function, and their combination. Vascular vs. non-vascular UNet architecture was compared. AP(ai)Bias 2.0-UNet was identified in these UNet classes based on (i) attributes of UNet architecture and its performance, (ii) explainable AI (XAI), and, (iii) pruning (compression). Five bias methods such as (i) ranking, (ii) radial, (iii) regional area, (iv) PROBAST, and (v) ROBINS-I were applied and compared using a Venn diagram. Findings and Conclusions: Vascular and non-vascular UNet systems dominated with sUNet classes with attention. The majority of the studies suffered from low interest in XAI and pruning strategies. None of the UNet models qualified to be bias-free. There is a need to move from paper-to-practice paradigms for clinical evaluation and settings. INDEX TERMS Image segmentation; vascular; non-vascular; UNet classes; UNet variations; UNetcomponents; explainable AI; pruning; bias.