Infants are exceptionally fragile and physically vulnerable who need special healthcare. Continuous monitoring of vital information of infants is essential for understanding their health status. Whereas modern infant health monitoring is carried out with dedicated facilities in controlled hospital settings, they are associated with several issues such as potential iatrogenic injuries, barriers for skin-to-skin parental bonding, and even complications during basic clinical tasks. Recently, soft electronics have become an accessory and mobile infant monitoring platform with remarkable advantages over existing technologies. This review comprehensively summarizes the research advances on soft electronics for advanced infant monitoring. We first introduce the physiological characteristics from anatomy, diseases, and treatments of infants. In accordance with these characteristics, we discuss the progressive achievements of soft bioelectrical, biophysical, biochemical, and hybrid monitoring technologies for infants. In addition, we offer insights into the remaining challenges and future directions of a soft electronics based intelligent system for clinical-grade infant monitoring from sensor design, data processing, power supply, and digital interactions in the era of Internet of Things. Finally, we highlight the translational challenges to be considered in bringing soft electronics for infant monitoring from the benchtop to the bedside.