This review covers the latest developments in continuous-variable quantum-state tomography of optical fields and photons, placing a special emphasis on its practical aspects and applications in quantum-information technology. Optical homodyne tomography is reviewed as a method of reconstructing the state of light in a given optical mode. A range of relevant practical topics is discussed, such as state-reconstruction algorithms (with emphasis on the maximum-likelihood technique), the technology of time-domain homodyne detection, mode-matching issues, and engineering of complex quantum states of light. The paper also surveys quantum-state tomography for the transverse spatial state (spatial mode) of the field in the special case of fields containing precisely one photon.

We have reconstructed the quantum state of optical pulses containing single photons using the method of phase-randomized pulsed optical homodyne tomography. The single-photon Fock state $|1〉$ was prepared using conditional measurements on photon pairs born in the process of parametric down-conversion. A probability distribution of the phase-averaged electric field amplitudes with a strongly non-Gaussian shape is obtained with the total detection efficiency of $(55\pm 1)\%$. The angle-averaged Wigner function reconstructed from this distribution shows a strong dip reaching classically impossible negative values around the origin of the phase space.

We employ the quantum state of a single photon entangled with the vacuum (|1,0>-|0,1>), generated by a photon incident upon a symmetric beam splitter, to teleport single-mode quantum states of light by means of the Bennett protocol. Teleportation of coherent states results in truncation of their Fock expansion to the first two terms. We analyze the teleported ensembles by means of homodyne tomography and obtain fidelities of up to 99 per cent for low source state amplitudes. This work is an experimental realization of the quantum scissors device proposed by Pegg, Phillips and Barnett (Phys. Rev. Lett. 81, 1604 (1998))

We produce a 600-ns pulse of 1.86-dB squeezed vacuum at 795 nm in an optical parametric amplifier and store it in a rubidium vapor cell for $1\mu \mathrm{s}$ using electromagnetically induced transparency. The recovered pulse, analyzed using time-domain homodyne tomography, exhibits up to $0.21\pm 0.04\mathrm{dB}$ of squeezing. We identify the factors leading to the degradation of squeezing and investigate the phase evolution of the atomic coherence during the storage interval.