This article describes the international safety standards that iPhone batteries meet.
Underwriters Laboratory (UL) 2054: Covers safety of lithium-ion batteries in general use.
UL 60950-1 and International Standard IEC/EN 60950: Cover the use of batteries in information-technology equipment.
Institute of Electrical and Electronics Engineers (IEEE) 1725: Covers safety of lithium-ion batteries used in cellular devices.
International Standard IEC 62133: Covers secondary cells and batteries containing alkaline or other nonacid electrolytes.
These standards meet the safety and testing criteria in the FAA Advisory Circular AC 120-76D regarding the airworthiness and use of portable electronic flight bags.