Fluorescent calcium sensors are widely used to image neural activity. Using structure-based mutagenesis and neuron-based screening, we developed a family of ultra-sensitive protein calcium sensors (GCaMP6) that outperformed other sensors in cultured neurons and in zebrafish, flies, and mice in vivo. In layer 2/3 pyramidal neurons of the mouse visual cortex, GCaMP6 reliably detected single action potentials in neuronal somata and orientation-tuned synaptic calcium transients in individual dendritic spines. The orientation tuning of structurally persistent spines was largely stable over timescales of weeks. Orientation tuning averaged across spine populations predicted the tuning of their parent cell. Although the somata of GABAergic neurons showed little orientation tuning, their dendrites included highly tuned dendritic segments (5 - 40 micrometers long). GCaMP6 sensors thus provide new windows into the organization and dynamics of neural circuits over multiple spatial and temporal scales.