Crossfire is primarily for Infantry combat. Less good for combined arms operations, definitely no good for big tank battles. A quick summary of Crossfire mechanics. No ranges - everything is is range all the time (except SMGs, which get a bonus only just before close combat) Visibility is not like normal wargames LOS. Instead it is all terrain feature to terrain feature. Some terrain does not block LOS, most does. The game relies on there being lots of terrain.

No game turns. So long as you have the initiative, you can keep on doing things indefinitely. Moving, firing, rallying, fighting close combats. Non-phasing play can use reactive fire on your squads, but once a squad has fired reactively and missed, it can't fire again till its owner gets initiative (this is a very important bit as it allows envelopments and other sneaky tactics)

But, if one of your actions fails, you lose initiative and your opponent gets it. Examples of failed actions:

1. Moving squad suppressed or killed by enemy reactive fire
2. Failure to suppress or kill enemy with fire
3. Failure to rally.

Firing is by rolling groups of d6. Normally 3 for a squad, 4 for a HMG.
deduct 1d6 if firing at people in cover.
Roll the dice looking for 5s and 6s 'hits'. 1 hit is a pin, 2 a suppress, 3 a kill.

Pinned squads can't move (but can go prone), but can fire. Suppressed squads can do nothing except try to rally.

Also, most nations (apart from the Germans and the Finns) must have sight of their commander to move (for Brits and Americans, at the start of their move, for Russians and some others, at both start and end). Commanders are also important for co-ordinating fire from separated squads ('crossfires').

There's also off-table indirect fire, which can either be HE or smoke.

You really need to try the game out to get a feel for what it's like. Most peoples' reaction is that it won't work, but it does. Also, it takes a while to get used to the tactics of fire and movement, use of smoke, and so on. It plays more like a description of a small unit battle than any other set of rules I've played, and it is fast. Every game we've played has been very exciting.