Apparatus for monitoring an infant comprises infant unit 2, arranged to be located near an infant, which includes a plurality of sensors 4 and a processing unit 20. The processing unit analyses sensory data from at least one of the sensors, algorithmically interprets the data, and autonomously responds directly at the infant unit and/or triggers a remote alarm at a wirelessly coupled parent unit 8. The processing unit may use a pre-trained machine learning algorithm such as a neural network to categorise different kinds of event from the sensor data. The accuracy of the machine learning algorithm may be reinforced by sensor data. The processing unit may analyse the frequency and amplitude characteristics of sound data received in the sensory data. The parent unit may include a user interface through which alarm thresholds can be adjusted. In a second aspect, apparatus for monitoring an infant includes an integrated projector capable of projecting video and images onto a surface.