Use of spectral/hp element methods, such as continuous or discontinuous Galerkin methods, in eddy-resolving computations of turbulent flows without turbulence models started to grow in popularity from about ten years ago and currently is a widespread strategy for high-fidelity flow simulation in academia, while gradually growing in industry applications as well. This approach is often referred to as implicit large-eddy simulation (iLES), where it is assumed that numerical dissipation implicitly plays the role of a turbulence model, thus providing results similar to traditional large-eddy simulation (LES). The rationale regarding why and how to use this approach is directly related to the underlying numerical dissipation of the discretisation. This talk will discuss the progress that has occurred in recent years regarding the rationale for this approach based on linear analyses of dispersive and diffusive numerical characteristics, as well as present applications to canonical and more complex flow cases [1,2,3,4]. In particular, comparisons between iLES and traditional LES will be shown for three test cases, namely: the transitional/turbulent Taylor-Green vortex, a spatially developing turbulent channel flow, and, as a more challenging test, a rotating turbulent boundary layer case proposed by P.R.Spalart to assess traditional LES models [5]. References: [1] R.C.Moura, S.Sherwin and J.Peiró. Linear dispersion-diffusion analysis and its application to under-resolved turbulence simulations using discontinuous Galerkin spectral/hp methods. Journal of Computational Physics, 298:695-710, 2015. [2] R.C.Moura, G.Mengaldo, J.Peiró and S.J.Sherwin. On the eddy-resolving capability of high-order discontinuous Galerkin approaches to implicit LES / under-resolved DNS of Euler turbulence. Journal of Computational Physics, 330:615-623, 2016. [3] G.Mengaldo, et al. Industry-relevant implicit large-eddy simulation of a high-performance road car via spectral/hp element methods. SIAM review, 63:723-755, 2021. [4] R.C.Moura, A.Cassinelli, A.F.C.Silva, E.Burman and S.J.Sherwin. Gradient jump penalty stabilisation of spectral/hp element discretisation for under-resolved turbulence simulations. Computer Methods in Applied Mechanics and Engineering, 388:114200, 2022. [5] P.R.Spalart. Theoretical and numerical study of a three-dimensional turbulent boundary layer. Journal of Fluid Mechanics, 205:319–340, 1989.