It is an exciting time for imaging in perinatal care. Technical advances in imaging technology mean that good quality clinical 3D ultrasound images of the growing fetus can be acquired from an early gestational age (GA) (11 weeks GA onwards). With the help of advances in MR-based reconstruction which compensate for fetal motion, high quality images of the fetal brain (and other organs) can be obtained which are providing, on the one hand exciting visualizations of the developing brain, as well as are leading to the introduction of fetal MRI into clinical practice for assessing the health of the fetus from around 24 weeks GA. The Oxford Biomedical Image Analysis Laboratory has been developing a program of research on image analysis for perinatal care over the last 3-5 years. This paper summarizes some of our recent published findings, and suggests some future directions of research.