Single-walled carbon nanotubes are uniquely identified by a pair of chirality indices (n, m), which dictate the physical structures and electronic properties of each species(1). Carbon nanotube research is currently facing two outstanding challenges: achieving chirality-controlled growth and understanding chirality- dependent device physics(2-6). Addressing these challenges requires, respectively, high-throughput determination of the nanotube chirality distribution on growth substrates and in situ characterization of the nanotube electronic structure in operating devices. Direct optical imaging and spectroscopy techniques are well suited for both goals(7-9), but their implementation at the single nanotube level has remained a challenge due to the small nanotube signal and unavoidable environment background(10-17). Here, we report high-throughput real-time optical imaging and broadband in situ spectroscopy of individual carbon nanotubes on various substrates and in field-effect transistor devices using polarization-based microscopy combined with supercontinuum laser illumination. Our technique enables the complete chirality profiling of hundreds of individual carbon nanotubes, both semiconducting and metallic, on a growth substrate. In devices, we observe that highorder nanotube optical resonances are dramatically broadened by electrostatic doping, an unexpected behaviour that points to strong interband electron-electron scattering processes that could dominate ultrafast dynamics of excited states in carbon nanotubes.