JohnR
"I always thought that decisions to divert to another airport due to crap weather, etc. were solely at the discretion of the captain? Do I infer from some answers on this thread that the airline ops department can have a say too?"
If the diversion is for something "routine" and not time critical then yes, Ops can, and probably would have a say. For example say you are heading into LHR from the States, but still hundreds of miles out, and the LHR weather goes below limits for an approach then a diversion is on the cards. Before diving into Cardiff/Shannon/Stansted/Gatwick or wherever it might be prudent for the Flight Crew to talk to Ops ( via Radio or Sat Comm) and ask them if they had a preference as to a landing airport. Ops will have the big picture information about the availability of Ground Handling/Fuel etc, etc. Having got Ops input the Captain would then be in a better position to make the decison as to where to divert to.
On the other hand if time and/or circumstances don't permit ( e.g. in-Flight Emergency involving a landing ASAP) you get the aircraft on the ground, hopefully at a suitable airfield, and then talk to Ops