Who believes what in IE linguistics?

In my studies of comparative Indo-European linguistics, I am somewhat
confused as to which scholars hold which views. I do gather, for
instance, that Szemerenyi disliked laryngeal theory, that Beekes
doubts the existence of phonemic *a and upholds glottalic theory, and
that Gamkrelidze and Ivanov won't accept anything unless typologically
probable. Still, how other scholars view these assertions is
unclear. Fortson, for instance, writes in his textbook that glottalic
theory has already been dismissed, but glottalic theory sure seems
popular in Mouton de Gruyter's recent collections of monographs.

Could someone please give a brief list of current "schools" of thought
in IE linguistics, what beliefs set each off from the others?

I'm especially curious as to beliefs on the precise nature of the
larygeals, who believes h1 was definitely a glottal stop, for example.

Christopher Culver