Understanding particle dynamics in turbulence is relevant to mixing, combustion, and environmental pollution. The study of transport by turbulent flows has benefited greatly from the development of new experimental, numerical, and theoretical Lagrangian techniques. These have made it possible to investigate the statistics of the velocity, the acceleration, and the dispersion of both tracer and inertial particles. While the early Lagrangian studies were mainly concerned with the motion of point particles, in recent years the study of particle dynamics in turbulent flows has extended in several new directions. The Colloquium aims at discussing the recent advances and the open questions in the area of complex particle dynamics in turbulent flows by gathering scientists from both the physics and engineering communities.