For the U.S. portion of your trip, the relevant regulation will be 14 CFR 175.10 (a)(18).
Here's the passenger-friendly, non-legalese summary version of the relevant CFR from the FAA:
Lithium ion batteries (a.k.a.: rechargeable lithium, lithium polymer, LIPO, secondary lithium). Passengers may carry all consumer-sized lithium ion batteries (up to 100 watt hours per battery). This size covers AA, AAA, cell phone, PDA, camera, camcorder, handheld game, tablet, portable drill, and standard laptop computer batteries. The watt hours (Wh) rating is marked on newer lithium ion batteries and is explained in #3 below. External chargers are also considered to be a battery.
With airline approval, devices can contain larger lithium ion batteries (101-160 watt hours per battery), but spares of this size are limited to two batteries in carry-on baggage only. This size covers the largest aftermarket extended-life laptop batteries and most lithium ion batteries for professional-grade audio/visual equipment. Most lithium ion batteries for consumer electronics are below this size.
Note that the FAA specifically states that LiPo batteries are included in this category and that the FAA limits are the same as the IATA limits mentioned in JoErNanO's answer. That is, the limits are:
- LiPo batteries installed in a device are ok in either checked or carry-on luggage.
- An unlimited number of spare (uninstalled) LiPo batteries with a rating of up to 100 WHr may be carried, but only in carry-on baggage.
- With airline approval, up to 2 LiPo batteries with ratings between 100 and 160 WHr may be carried, but only in carry-on luggage.
- LiPo batteries larger than 160 WHr are not allowed.
Packing instructions
Note also that the same FAA document states that:
Spare batteries must be protected from damage and short circuit.
Battery-powered devices must be protected from accidental activation and heat generation.
Chargers
Another important thing to note from that document is that they consider external chargers as if they were batteries and, as such, those are only allowed in carry-on luggage, not in checked luggage.
The second page of the document contains a table to help clarify what is allowed and where.
