While the radio spectrum allocation is well regulated, there is little knowledge about its actual utilization over time and space. This limitation hinders taking effective actions in various applications including cognitive radios, electrosmog monitoring, and law enforcement. We introduce Electrosense, an initiative that seeks a more efficient, safe and reliable monitoring of the electromagnetic space by improving the accessibility of spectrum data for the general public. A collaborative spectrum monitoring network is designed that monitors the spectrum at large scale with low-cost spectrum sensing nodes. The large set of data is stored and processed in a big data architecture and provided back to the community with an open spectrum data as a service model, that allows users to build diverse and novel applications with different requirements. We illustrate useful usage scenarios of the Electrosense data.