Turbulent motions are ubiquitous and impact almost every aspect of our life, from the formation of hurricanes to the mixing of a cappuccino. The mathematical description of turbulent flows is established, and in the last four decades computational tools have been used extensively to increase our understanding of the basic physical processes as well as to improve the design of engineering devices. The multiscale nature of turbulence creates unique challenges for numerical simulations. Discretization methods must preserve the physical processes, reducing or eliminating artificial dissipation and dispersion. Moreover, the extreme computational effort required to capture all the temporal and spatial scales of motion leads to the introduction of physical models for unresolved features. How do you establish confidence in the numerical simulations of turbulent flows? The talk will describe how the concepts of verification, validation and uncertainty quantification are developed and used in the framework of turbulence simulations. Several applications of turbulent flow simulations will also be described ranging from turbulent combustion in jet engines to aero-acoustics.