In the last decades, a wide range of attractive properties have put metallic nanoparticles in the spotlight. These properties, often related to optical response and catalytic performance, are to a large extent dependent on structure and chemical ordering, that is, the distribution of elements in the nanoparticle. To better understand and predict the behavior of such particles, a thorough understanding of these parameters is essential. This thesis investigates structure and chemical ordering in metal nanoparticles using atomistic modeling based on molecular dynamics and Monte Carlo simulations with embedded atom method potentials. The thesis describes frequently occurring nanoparticle structures and discusses the importance for an atomistic perspective in relation to the existence of magic and non-magic numbers in particles with different shapes. Further, alloy thermodynamics and key differences and similarities between macroscopic and microscopic systems are reviewed from a statistical mechanics perspective. The thesis highlights the importance for comprehensive investigations of the size and composition parameters to obtain a coherent picture. In particular, it is shown how recognition of polydisperse nanoparticle ensembles is crucial to predict the distribution of nanoparticle shapes in thermodynamic equilibrium and how the distribution of elements in an alloy nanoparticle is intimately connected to the underlying structure.