Summation-by-parts (SBP) operators, which discretely mimic the integration-by-parts principle, provide a systematic framework for constructing energy-stable numerical methods for energy-bounded initial boundary value problems (IBVPs). Initially developed for finite difference schemes with polynomial approximations to achieve energy-stable semi-discretizations, significant advancements have emerged over the past decade. These include generalized and hybrid SBP operators for arbitrary grids, SBP operators on point clouds, upwind SBP operators, and the broader class of function-space SBP operators. This talk provides an overview of recent developments in SBP operators and their applications in numerical methods for advection-dominated problems. Particular attention is given to upwind SBP operators and function-space SBP operators, highlighting advancements in their construction and demonstrating their versatility across various settings, including finite difference (FD), discontinuous Galerkin (DG), and mesh-free approaches.