Mobile robots behaving as humans should possess multifunctional flexible sensing systems including vision, hearing, touch, smell, and taste. A gas sensor array (GSA), also known as electronic nose, is a possible solution for a robotic olfactory system that can detect and discriminate a wide variety of gas molecules. Artificial intelligence (AI) applied to an electronic nose involves a diverse set of machine learning algorithms which can generate a smell print by analyzing the signal pattern from the GSA. A combination of GSA and AI algorithms can empower intelligent robots with great capabilities in many areas such as environmental monitoring, gas leakage detection, food and beverage production and storage, and especially disease diagnosis through detection of different types and concentrations of target gases with the advantages of portability, low-power-consumption and ease-of-operation. It is exciting to envisage robots equipped with a "nose" acting as family doctor who will guard every family member's health and keep their home safe. In this review, we give a summary of the state-of the-art research progress in the fabrication techniques for GSAs and typical algorithms employed in artificial olfactory systems, exploring their potential applications in disease diagnosis, environmental monitoring, and explosive detection. We also discuss the key limitations of gas sensor units and their possible solutions. Finally, we present the outlook of GSAs over the horizon of smart homes and cities.