While there has been substantial progress in segmenting natural im-ages, state-of-the-art methods that perform well in such tasks unfortunately tend to underperform when confronted with the different challenges posed by electron microscope (EM) data. For example, in EM imagery of neural tissue, numerous cells and subcellular structures appear within a single image, they exhibit irregular shapes that cannot be easily modeled by standard techniques, and confusing textures clutter the background. We propose a fully automated approach that handles these challenges by using sophisticated cues that capture global shape and texture information, and by learning the specific appearance of object boundaries. We demonstrate that our approach significantly outperforms state-of-the-art techniques and closely matches the performance of human annotators.