Active matter has become a lively topic in recent years, but what exactly is meant by the term ‘active matter’ is often unclear. This Colloquium discusses the scientific and semantic issues underlying this ambiguity, as well as the history of the field, and offers a definition of active matter as a well-defined subset of nonequilibrium systems. It then surveys recent developments including nonreciprocal interactions, intracellular phase separation, and quantum active matter.

Recent advances in molecular cooling have enabled the realization of strongly dipolar molecular Bose-Einstein condensates. Such systems provide a unique platform for investigating new states of matter, from quantum droplets to supersolids. This Colloquium surveys the collisional shielding techniques that make stable molecular condensates possible, the theoretical challenges that arise in the strongly dipolar regime, and the exotic quantum phases now within experimental reach.

Coulomb crystals form when the Coulomb interaction between charged particles dominates over kinetic energy; the prototype is the Wigner crystal formed by conduction electrons in metals at low densities. In recent years, it has become possible to realize Coulomb crystals using laser-cooled trapped ions, and these systems allow for unprecedented control of experimental parameters. This review describes the state of the art of ion Coulomb crystals in one, two, and three dimensions, their properties in and out of equilibrium, and their importance across fields ranging from condensed matter to astrophysics.

The polaron, a single impurity embedded in a quantum many-body environment, conceptually bridges few- and many-body physics. Its properties provide both a test bed for many-body theories and physical insight into the phase structure of more complicated many-body systems. This review discusses two pristine experimental platforms in which polarons have recently been realized: ultracold atomic gases and atomically thin transition-metal dichalcogenides. The authors discuss the theory of Bose and Fermi polarons, compare theory to experiment, and provide a perspective on how polarons may serve as precise sensors in complex environments.

It is sometimes said that if one uses quantum cryptography methods to distribute keys, their secrecy is guaranteed by the laws of physics. This is only partly true: while quantum physics provides a strong boost to security, the proper mathematical analysis of the full detailed protocol is still nontrivial. This review provides details of this analysis for one of the most important quantum protocols for key distribution and its variants, in which weak (few photon) coherent pulses are transmitted and threshold detectors are used for measurements.

Social systems, when considered on an appropriately coarse-grained scale, display phenomena reminiscent of the behavior of physical many-body systems and can be studied using the methods of statistical mechanics. A particularly interesting subfield is opinion dynamics, which aims to understand the emergence of collective social phenomena, such as consensus, polarization, and fragmentation. This review systematizes the terminology and methods of opinion dynamics, surveys empirical findings alongside theoretical models, and summarizes the current state and future directions of this field.