I can't comment on the military application.
RE: LE however:
Other than what Jeff has contributed:
LAPD is the agency that did the study documenting the extent of grappling encounters occurring during police confrontations. After this they instituted a curriculum based heavily in ground grappling tactics (some better than others I might add). Over the next few years they realized a reduction in suspect injuries, officer injuries, lawsuits, and time off for injury claims at at time when attacks against officers grew more violent.
Then there is LVNR, a Judo based DT method involving takedowns and ground tactics, proven extremely effective in practical application starting in Kansas City and now moving through the country.
ISR matrix is a clinch and ground grappling based LE method devised by a police officer and a bouncer with extensive background in wrestling, judo and BJJ.
Hell, even the latest issue of SWAT magazine contains an article about a grappling system for LE which, after railing against the "jujitsu guard" and the "clench" and NHB fighting shows clinch work and ground grappling that is clearly adapted from the clinch and ground stuff common in any judo, BJJ, or sub wrestling club today.
The point is law enforcement has realized, and rightly so, that real fighting involves a great deal of clinching and groundwork (moreso for cops since apprehension is the goal in the vast majority of situations - but in my experience responding to all manner of assaults and fights and interviewing participants and victims, at least 40-50% of violent situations involve one or both parties on the ground with the fight continuing.) Watch a number of "car cam" videos of officer involved altercations, and especially in the most dangerous/lethal confrontations a large percentage of them spend some time on the ground.
Of course what we are talking about is not straight mat-style judo, BJJ, sub wrestling or what have you. ANY fighting art has to be adapted to the REAL weapons based close quarters environment and it has to be applied in a manner that will successfully deal with everything from the arrest of a low risk, uncooperative drunk elderly person to a multiple assailant ambush by gangbangers.
Most people have little or no experience actually doing so with their art, and no frame of reference for what various close confrontations at different levels of force (in civil life at least) are actually like. Even less do they understand the realities of police response to the same kind of thing.
Suffice it to say, a LOT of grappling happens. Standing in the clinch and on the ground whether on top or on the bottom. A thorough grounding in strategies and tactics based in judo, BJJ, and wrestling, adapted for the realities of "the street," is a very strong component of police control and survival training today.