  This review serves as a concise introductory survey of modern compressive
tomography developed since 2019. These are schemes meant for characterizing
arbitrary low-rank quantum objects, be it an unknown state, a process or
detector, using minimal measuring resources (hence compressive) without any
\emph{a priori} assumptions (rank, sparsity, eigenbasis, \emph{etc}.) about the
quantum object. This article contains a reasonable amount of technical details
for the quantum-information community to start applying the methods discussed
here. To facilitate the understanding of formulation logic and physics of
compressive tomography, the theoretical concepts and important numerical
results (both new and cross-referenced) shall be presented in a pedagogical
manner.
