Metal nanoparticles have been widely used as functional materials in physics, chemistry, and biology. Understanding their unique thermodynamic properties is essential both for practical applications and from a fundamental point of view. This perspective article is an overview of recent progresses on the nanothermodynamics of metal nanoparticles and it especially highlights as examples our own studies on the structural stability, phases, phase changes, and thermodynamic functions of aluminum nanoparticles. We discuss using statistical sampling by Monte Carlo and molecular dynamics algorithms to calculate nanoparticle properties, nanophase properties, free energies, and nucleation rates, and we tried to understand the results in terms of energy landscapes by using exhaustive enumeration of the multiple structures of Al nanoparticles from all sizes up to N = 65 plus selected larger calculations.