Ion Coulomb crystals are ordered structures formed by laser-cooled ions in traps that are characterized by interparticle distances of several micrometers and energy scales on the order of $\mathrm{\mu }\mathrm{eV}$. Their crystalline structure emerges from the interplay between Coulomb repulsion and the external confining potential, which can be readily tuned. Moreover, individual ions can be precisely manipulated with lasers and imaged via resonance fluorescence. These unusual and unique properties make ion crystals a powerful platform for studying phases of matter in the strongly correlated regime and at low temperatures where their dynamics is manifestly quantum mechanical. This review examines the theoretical framework and experimental characterization of ion Coulomb crystals from a condensed-matter perspective. Their dynamical and thermodynamic properties are discussed in one, two, and three dimensions, and recent investigations into their out-of-equilibrium behavior are reviewed. An outlook on future directions for exploring novel condensed-matter phenomena with trapped-ion crystals, as well as for exploiting these features for scientific and technical applications, is provided.

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• Friction
• Quantum phase transitions
• Structural phase transition
• Crystalline systems
• Nonequilibrium systems
• Single-component plasmas
• Trapped ions
• Wigner crystal