  The emergence of active regions on the Sun is an integral feature of the
solar dynamo mechanism. However, details about the generation of
active-region-scale magnetism and the journey of this magnetic flux to the
photosphere are still in question. Shifting paradigms are now developing for
the source depth of the Sun's large-scale magnetism, the organization of this
magnetism into fibril flux tubes, and the role of convection in shaping
active-region observables. Here we review the landscape of flux emergence
theories and simulations, highlight the role flux emergence plays in the global
dynamo process, and make connections between flux emergence on the Sun and
other cool stars. As longer-term and higher fidelity observations of both solar
active regions and their associated flows are amassed, it is now possible to
place new constraints on models of emerging flux. We discuss the outcomes of
statistical studies which provide observational evidence that flux emergence
may be a more passive process (at least in the upper convection zone);
dominated to a greater extent by the influence of convection and to a lesser
extent by buoyancy and the Coriolis force acting on rising magnetic flux tubes
than previously thought. We also discuss how the relationship between stellar
rotation, fractional convection zone depth, and magnetic activity on other
stars can help us better understand flux emergence processes. Looking forward,
we identify open questions regarding magnetic flux emergence that we anticipate
can be addressed in the next decade with further observations and simulations.
