Patients in the Neonatal Intensive Care Unit (NICU) have high mortality and morbidity rates due to their low birth weight or being preterm. Due to their vulnerability, neonates require close monitoring so that timely treatment can be performed. However, current, state-of-the-art technologies for continuous vital sign monitoring in the NICU are not optimal due to the use of wires and adhesives. Wires impede the natural movement of neonates, disallow intimate kangaroo care, and impose inconvenience on daily caretaking. The use of adhesives can damage neonates’ skin during removal. To address these problems, many wearable systems or contactless setups have been proposed for their respective vital signs. In this review, an overview of these newer technologies, along with their working principles, is discussed.