Fusion performance in tokamaks depends on the core and edge regions as well as on their nonlinear feedbacks. The achievable degree of edge confinement under the constraints of power handling in presence of a metallic wall is still an open question. Therefore, any improvement in the core temperature and density peaking is crucial for achieving target performance. This has motivated further progress in understanding core turbulent transport mechanisms, to help scenario development in present devices and improve predictive tools for ITER operations. In the last two decades, detailed experiments and their interpretation via the gyrokinetic theory of turbulent transport have led to a satisfactory level of understanding of the heat, particle, and momentum transport channels and of their mutual interactions. This paper presents some highlights of the progress, which stems from joint work of several devices and theory groups, in Europe and worldwide within the International Tokamak Physics Activities framework. On the other hand, the achievement of predictive capabilities of plasma profiles via integrated modeling, which also accounts for the nonlinear interactions inherent to the multi-channel nature of transport, is a priority in view of ITER. This requires using faster, reduced models, and the extent to which they capture the complex physics described by nonlinear gyrokinetics must be carefully evaluated. Present quasi-linear models match well experiments in baseline scenarios, and thus offer reliable predictions for the ITER reference scenario, but have issues in advanced scenarios. Some of these challenges are examined and discussed. In the longer term, advances in high performance computing will continue to drive physics discovery through increasingly complex gyrokinetic simulations, allowing also further development of reduced models. The development of neural network surrogate models is another recent advance that bridges the gap towards physics-based fast models for optimization and control applications.