Many people seem to be worried about this, but first think... what is powering your iphone?... a Lipo and your ipad?... a Lipo and your PC? a Lipo. So you already travel by air with Lipos. There are some rules that are easy to be followed. In case a controller asks about your lipo, explain it is RC model battery with the same technology as the one in any laptop, usually it is the end of the discussion.
Because of the risk of fire, you are not allowed to transport lipos in your checked luggage. Immagine a fires starts in the plane luggage compatment, nobody can take appropriate actions. Many of us have seen the restriction applied for fret Lipos, for example ordering Lipos from Asian RC stores.
Regarding Carry-on transport of our propulsion Lipos, some restriction apply for so-called "larger batteries" usually above 8g equivalent Lithium (100 Watt-hours) and no battery above 25 g equivalent Lithium (300 Watt-hours) are allowed. You can carry 2 "Larger batteries" them in your carry-on luggage, each have to contain less that 25g equivalent Lithium which is about 300 watt-hour.
If you don't know about watt-hours, you can calculate yourself using the formula:
mAh/1000 x V = wh
So my 3300 mAh - 4S batteries are (3300/1000) x 14.8 = 48.8 Watt-hours ... below 100 are not "Larger batteries" and are normally not restricted in carry on luggage. I travelled to Brasil, USA, different locations in Europe, French Polynesia (via LA) with about 8 to 10 Lipos in my bag without any problem. Sometimes I had to explain that it is RC batteries and once that it is rechargeable (non-rechargeable Lithium batteries are forbidden).
Now take a 5000 mAh - 6S battery for a big Hexacopter: (5000/1000)x22.2 = 111 Watt-hours ... above 100, this are limited to two per person in the carry-on!
Make sure you check with your airline if they don't have specific rules !
Here are links for more details: