Introduction: The aim of this study was to develop a pipeline using state-of-the-art deep learning methods to automatically delineate and measure several of the most important brain structures in fetal brain ultrasound (US) images. Methods: The dataset was composed of 5,331 images of the fetal brain acquired during the routine mid-trimester US scan. Our proposed pipeline automatically performs the following three steps: brain plane classification (transventricular, transthalamic, or transcerebellar plane); brain structures delineation (9 different structures); and automatic measurement (from the structure delineations). The methods were trained on a subset of 4,331 images and each step was evaluated on the remaining 1,000 images. Results: Plane classification reached 98.6% average class accuracy. Brain structure delineation obtained an average pixel accuracy higher than 96% and a Jaccard index higher than 70%. Automatic measurements get an absolute error below 3.5% for the four standard head biometries (head circumference, biparietal diameter, occipitofrontal diameter, and cephalic index), 9% for transcerebellar diameter, 12% for cavum septi pellucidi ratio, and 26% for Sylvian fissure operculization degree. Conclusions: The proposed pipeline shows the potential of deep learning methods to delineate fetal head and brain structures and obtain automatic measures of each anatomical standard plane acquired during routine fetal US examination.