Semantic segmentation for robotic systems can enable a wide range of applications, from self-driving cars and augmented reality systems to domestic robots. We argue that a spherical representation is a natural one for egocentric pointclouds. Thus, in this work, we present a novel framework exploiting such a representation of LiDAR pointclouds for the task of semantic segmentation. Our approach is based on a spherical convolutional neural network that can seamlessly handle observations from various sensor systems (e.g., different LiDAR systems) and provides an accurate segmentation of the environment. We operate in two distinct stages: First, we encode the projected input pointclouds to spherical features. Second, we decode and back-project the spherical features to achieve an accurate semantic segmentation of the pointcloud. We evaluate our method with respect to state-of-the-art projection-based semantic segmentation approaches using well-known public datasets. We demonstrate that the spherical representation enables us to provide more accurate segmentation and to have a better generalization to sensors with different field-of-view and number of beams than what was seen during training.