The stability and frequency content of local field potentials (LFPs) offer key advantages for long-term, low-power neural interfaces. However, interpreting LFPs may require new signal processing techniques which should be informed by a scientific understanding of how these recordings arise from the coordinated activity of underlying neuronal populations. We review current approaches to decoding LFPs for brain-machine interface (BMI) applications, and suggest several directions for future research. To facilitate an improved understanding of the relationship between LFPs and spike activity, we share a dataset of multielectrode recordings from monkey motor cortex, and describe two unsupervised analysis methods we have explored for extracting a low-dimensional feature space that is amenable to biomimetic decoding and biofeedback training.