The presence of nonlinear instabilities poses a significant challenge in the context of turbulence simulation. In both compressible and incompressible flows, the preservation of kinetic energy has been shown to mitigate the stability issue that is due to the accumulation of the aliasing error. This idea of reproducing key features of the continuous equations in the discrete setting has been found to be of more general applicability than just the preservation of kinetic energy; for this reason, research has focused on the development of so-called structure-preserving methods. These discretizations are capable of preserving invariants and symmetries which would be lost otherwise. In the compressible case, additional care must be taken to ensure the correct evolution of thermodynamic variables to prevent nonphysical behavior and maintain stability. This presentation will explore the design of structure-preserving methods for shock-free compressible flows, tracing their evolution from classical kinetic-energy--preserving discretizations to more recent approaches that incorporate additional physical constraints. Entropy-conservative schemes ensure a consistent discrete entropy balance which increases physical fidelity of the simulation. Another considerable property is that of pressure-equilibrium preservation which originally arose in the context of multi-component gases, but it has been shown to be valuable also for simulations of single-species calorically perfect gases. In fact, its absence can be source of spurious oscillations of pressure. The effectiveness of these methods will be discussed through the analysis of several test cases. Finally, the potential computational overhead associated with structure-preserving methods will be addressed, exploring strategies to reduce their cost without compromising accuracy.