  We present in a unified manner the existing methods for scalable partial
quantum process tomography. We focus on two main approaches: the one presented
in Bendersky et al. [Phys. Rev. Lett. 100, 190403 (2008)], and the ones
described, respectively, in Emerson et al. [Science 317, 1893 (2007)] and
L\'{o}pez et al. [Phys. Rev. A 79, 042328 (2009)], which can be combined
together. The methods share an essential feature: They are based on the idea
that the tomography of a quantum map can be efficiently performed by studying
certain properties of a twirling of such a map. From this perspective, in this
paper we present extensions, improvements and comparative analyses of the
scalable methods for partial quantum process tomography. We also clarify the
significance of the extracted information, and we introduce interesting and
useful properties of the $\chi$-matrix representation of quantum maps that can
be used to establish a clearer path toward achieving full tomography of quantum
processes in a scalable way.
