The transportation of batteries by passengers is controlled by IATA, ICAO, DOT and other similar bodies. See summary for "dry cells" at end of this answer.
A number of freight handling and courier organisations make glossy publications available which summarise the rules. Individual airlines have their own requirements but generally will accept carriage of batteries by passengers if you pack them competently in your carry on baggage AND carry documentation listing ICAO requirements and waivers.
As a rule (and usually a specific airline rule), batteries such as AA or AA cells, camera, computer & phone batteries should be carried in carryon baggage and NOT in checked baggage. [Where would you rather have a fire start during your flight?].
Lithium batteries (both primary/non-rechargeable and secondary/rechargeable) may be carried but their is an upper limit to the equivalent amount of metallic Lithium that may be carried. Lithium grams equivalent per battery mAh figures are available. Most people will not come close to this limit but if you carry several laptops, extensions batteries for these, several cameras and many spare Li camera batteries it is possible to approach the limit. Ask me how I know :-).
There are exemptions which allow carriage of batteries in checked luggage. (Genuinely) sealed leak proof lead acid batteries may be carried in checked luggage if their outer wrapper contains a statement that they are exempt under ICAO regulations and quoting the exemption number. I have transported batteries in this manner and found signs afterwards that te bags have been opened and the battery checked. If it had not been labelled appropriately it would probably have been confiscated.
Batteries that are carried that are not in equipment should be either tape wrapped so shorting is impossible or in a robust container that maintains them in a short proof relative orientation.
Fedex and DHL have documents describing what batteries are able to be carried and how they need to be wrapped or isolated. If you cannot show them and/or quote them their own documentation they may refuse to carry batteries - even if inside equipment. Ask me how I know.
CHINA: When transporting batteries out of China by DHL or Fedex or other carrier using air freight the documentation applicable in other countries DOES NOT apply. To transport batteries by courier or air carrier out of China you need a certification from an authorised test house that the batteries meet certain regulatory requirements and tht they are packed properly. I have had a shipment of batteries fail to meet a holiday cutoff date due to lack of such documentation. While this requirement may sound like bureacratic overkill it is robably based on a desire top not have aeroplanes falling burning from the sky on too many occasions. China is so vast and market practices are so varied that it is impossible to trust the veracity or safety of any claim that is not backed either by iron tight official process or by systems that you have personally established that you can trust.
The restrictions for China do not apply to Hong Kong. If you can land transport batteries into HK and can satisfy yourself that they are packed in a safe and competent manner and are inherently safe then you can usually get Fedex or DHL etc to carry them. Ask me how I know :-).
I have had battery samples sent to me from China inside a toy or similar where the toy's purpose in this situation is solely to act as a battery carrier. This MAY work out of China proper (they came from Guangjho Dongguan area) but they MAY have been hand carried into HK by a staff member.
BST are one of the big-3 Chinese consumer battery makers (BST, BYD, GP). The following applies to their batteries outside China.
BST batteries say:
Section XIV -- Transportation Information
BST batteries are considered to be "Dry Cell" batteries and are unregulated for purposes of transportation by the U.S. Department of Transportation (DOT), International Civil Aviation Adminitration (ICAO), International Air Transport Association (IATA) and International Maritime Dangerous Goods Regulations (IMDG).
The only DOT requirement for shipping these batteries is special provision 130 which states:"Batteries, dry are not subject to the requirements of this subchapter only when they are offered for transportation in a manner that prevents the dangerous evolution of heat (For example,by the effective insulation of exposed terminals).
IATA is Special Provision A123 i.e. "An electrical battery or battery powered device having the potential of dangerous evolutions of heat that is not prepared so as to prevent a short-circuit(e.g. in the case of batteries,by the effective insulation of exposed terminals) is forbidden from transportation". As of 1/1/97 IATA requires that batteries being transported by air must be protected from short circuiting and protected from movement that could lead to short-circuiting with special provision 304 of IMDG.
UPS - How to safely pack and ship batteries
They note -
As you review this brochure, please be aware of how your
shipping practices comply with the guidance given here,
and understand that some of your batteries may require
you to review and comply with the
U.S. Department of Transportation
(DOT) Hazardous Materials Regulations (Title 49
of the Code of Federal Regulations) and/or
the International Air Transport Association (IATA) Dangerous Goods Regulations
The IATA DGR is based on and produced in consultation
with the International Civil Aviation Organization (ICAO)
Additionally, other international regulatory
requirements apply, such as the International Maritime
Dangerous Goods (IMDG) Code, and the ADR Dangerous
Goods Regulations for European Road Transport.
UPS- shipping batteries or devices with batteries
UPS - International Lithium Battry Regulations
PRBA - transporting batteries
DOT - Shipping batteries safely by air
DOT - shipping batteries safely - what you need to know
IATA - 2013 regs - Lithium battery guidance document
- This document is based on the provisions set out in the 2013-2014 Edition of the ICAO Technical Instruction for the Safe Transport of Dangerous Goods by Air and the 54th Edition of the IATA Dangerous Goods Regulations (DGR).
Fewdex - packing guidelines for battery shipments
USPS total bn on shipping Lithium batteries as of May 2012
Battery University - how to transport batteries
Carry-on limiting factor:
Battery QUANTITY is not the limiting carry-on factor.
For Lithium batteries it's the metallic Lithium content.
For others it's the carry-on weight allowance. I have carried 200+ AA rechargeable batteries as carryon on several occasions. At that stage they get me to take them out and XRAY them separately and inspect them as they are XRAY dense.