Here, we introduce Z-webs, including Z-factors and Z-nodes, for the understanding of relationships between objects, subjects, abstract ideas, concepts, or the like, including face, car, images, people, emotions, mood, text, natural language, voice, music, video, locations, formulas, facts, historical data, landmarks, personalities, ownership, family, friends, love, happiness, social behavior, voting behavior, and the like, to be used for many applications in our life, including on the search engine, analytics, Big Data processing, natural language processing, economy forecasting, face recognition, dealing with reliability and certainty, medical diagnosis, pattern recognition, object recognition, biometrics, security analysis, risk analysis, fraud detection, satellite image analysis, machine generated data analysis, machine learning, training samples, extracting data or patterns (from the video, images, and the like), editing video or images, and the like. Z-factors include reliability factor, confidence factor, expertise factor, bias factor, and the like, which is associated with each Z-node in the Z-web.