A fully automatic technique for segmenting the liver and localizing its unhealthy tissues is a convenient tool in order to diagnose hepatic diseases and also to assess the response to the according treatments. In this thesis we propose a method to segment the liver and its lesions from Computed Tomography (CT) scans, as well as other anatomical structures and organs of the human body. We have used Convolutional Neural Networks (CNNs), that have proven good results in a variety of tasks, including medical imaging. The network to segment the lesions consists of a cascaded architecture, which first focuses on the liver region in order to segment the lesion. Moreover, we train a detector to localize the lesions and just keep those pixels from the output of the segmentation network where a lesion is detected. The segmentation architecture is based on DRIU [24], a Fully Convolutional Network (FCN) with side outputs that work at feature maps of different resolutions, to finally benefit from the multi-scale information learned by different stages of the network. Our pipeline is 2.5D, as the input of the network is a stack of consecutive slices of the CT scans. We also study different methods to benefit from the liver segmentation in order to delineate the lesion. The main focus of this work is to use the detector to localize the lesions, as we demonstrate that it helps to remove false positives triggered by the segmentation network. The benefits of using a detector on top of the segmentation is that the detector acquires a more global insight of the healthiness of a liver tissue compared to the segmentation network, whose final output is pixel-wise and is not forced to take a global decision over a whole liver patch. We show experiments with the LiTS dataset for the lesion and liver segmentation. In order to prove the generality of the segmentation network, we also segment several anatomical structures from the Visceral dataset.