  We review recent progress in the electronic structure study of intrinsic
magnetic topological insulators (MnBi$_2$Te$_4$)(Bi$_2$Te$_3$)$_n$
($n=0,1,2,3$) family. Specifically, we focus on the ubiquitously (nearly)
gapless behavior of the topological surface state Dirac cone observed by
photoemission spectroscopy, even though a large Dirac gap is expected because
of surface ferromagnetic order. The dichotomy between experiment and theory
concerning this gap behavior is perhaps the most critical and puzzling question
in this frontier. We discuss various proposals accounting for the lack of
magnetic effect on the topological surface state Dirac cone, which are mainly
categorized into two pictures, magnetic reconfiguration, and topological
surface state redistribution. Band engineering towards opening a magnetic gap
of topological surface states provides great opportunities to realize quantized
topological transport and axion electrodynamics at higher temperatures.
