Large-scale integration of emerging nanoscale non-volatile memory devices, e.g. resistive random-access memory (RRAM), can enable a new generation of neuromorphic computers that can solve a wide range of machine learning problems. Such hybrid CMOS-RRAM neuromorphic architectures will result in several orders of magnitude reduction in energy consumption at a very small form factor, and herald autonomous learning machines capable of self-adapting to their environment. However, the progress in this area has been impeded from the realization that the actual memory devices fall well short of their expected behavior. In this work, we discuss the challenges associated with these memory devices and their use in neuromorphic computing circuits, and propose pathways to overcome these limitations by introducing 'dendritic learning'.