Right from the beginning, you'll be able to attempt to tame any critter you capture that is eligible (those with PET/PET_EXOTIC, i.e. most stuff). The trick will be that if you go out of your civilization's comfort zone, your fort might end up like a Fatal Attractions episode.
So, it appears that any valid creature may be tamed in the next release, including dragons - with some effort. It's alright though, we have a number of migrants who can die in the process of gleaning knowledge of the creatures and understanding their nature. This also includes certain creatures like Hydra and Roc that could be... interesting, to say the least.
How do we perform this best, and how do we weaponize it?
From Toady's post, it sounds like failed taming attempts may lend to escaped animals which may or may not attack dwarves depending on what kind of animal. Thus, my exotic taming pin will likely be a circular arena setting with the cage in the middle and cage traps over the door (webbed if needed). The dwarf will enter, and attempt a tame. If successful, the creature is tamed. If failed, the dwarf flees and/or dies, while the creature runs out and gets caged once more. Repeat until success. Once enough "Civilization Knowledge" is gathered on the beast, then your career tamer can start taming them instead of useless migrants.
The breeding is trickier. Dragons breed fairly quick-ish, but they take 1,000 years to mature, and we don't know how long an egg takes to hatch. Hydra do not appear to breed at all. Sea serpents take 6 years to mature, although they are egglayers and we currently assume that nest boxes cease function underwater (untested). Sea Monsters actually appear to have no gender, and thus no breeding, although they DO have a child count, strangely... The Roc matures in 1 year, with a value multiplier of 15, but a fairly massive egg that probably takes decades to hatch. Most of the other fun creatures (minotaur, giants, mermaids, bronze colossi) can't be tamed, at least in this version. Toady may update the raws to make them exotics. Regardless of all this, slight modding can be done to ensure childbearing.
Although once we are breeding animals... what would be done with them? Many of them are highly valuable pets, not to mention that a great number are powerful creatures of war, and some are mounts. Mounts currently can't be used, but in the future this sort of thing will prove valuable, so getting the knowledge now will do more good than harm.