Optical coherence tomography (OCT) based measurements of retinal layer thickness, such as the retinal nerve fibre layer (RNFL) and the ganglion cell with inner plexiform layer (GCIPL) are commonly employed for the diagnosis and monitoring of glaucoma. Previously, machine learning techniques have relied on segmentation-based imaging features such as the peripapillary RNFL thickness and the cup-to-disc ratio. Here, we propose a deep learning technique that classifies eyes as healthy or glaucomatous directly from raw, unsegmented OCT volumes of the optic nerve head (ONH) using a 3D Convolutional Neural Network (CNN). We compared the accuracy of this technique with various feature-based machine learning algorithms and demonstrated the superiority of the proposed deep learning based method. Logistic regression was found to be the best performing classical machine learning technique with an AUC of 0.89. In direct comparison, the deep learning approach achieved a substantially higher AUC of 0.94 with the additional advantage of providing insight into which regions of an OCT volume are important for glaucoma detection. Computing Class Activation Maps (CAM), we found that the CNN identified neuroretinal rim and optic disc cupping as well as the lamina cribrosa (LC) and its surrounding areas as the regions significantly associated with the glaucoma classification. These regions anatomically correspond to the well established and commonly used clinical markers for glaucoma diagnosis such as increased cup volume, cup diameter, and neuroretinal rim thinning at the superior and inferior segments.