A number of challanges and open questions remain. For instance, models of the full life-cyle of active regions from birth to decay remain to be developed. Such models may settle long standing questions about the depth from which active region fields are spawned which, in turn, tells us something about how the dynamo-generated magnetic field is structured in the convection zone. The decay of ARs is also an important topic that needs to be addresssed since the turbulent diffusion of AR-flux over the solar surface and the subduction of flux back into the convection zone likely determine how much remnant flux can be replenished for the large-scale dynamo field.
Helioseismic analysis of pre-emerging flux regions is still a nascent field. Numerical models are needed in order to validate helioseismic techniques which, in turn, are used on real observations to constrain numerical models. Continued work in this regard is likely essential for answering the question of whether we can robustly infer subsurface properties of emerging ARs well before their appearance at the surface.
In the near future, we anticipate substantial developments in data-driven models of emerging flux. Such models will use observed magnetogram sequences for boundary conditions of 3D MHD models. With such models, synthetic diagnostics can be directly compared with observations. Success in reproducing observables that quantatively match observations is crucial for a critical assessment of the maturity of MHD models. Furthermore, advances in this realm are essential for novel approaches to space weather forecasting that go beyond the use of heuristics and probabilistic models.