Air law is a diverse area although most specialist air law firms/departments tend to focus most on aircraft finance, because it is lucrative financially and there is a large, growing fleet of aircraft in the world.
Aviation accident claims accounts for most of the rest of the work. This is is directly linked to the insurance industry in two distinct ways; claims for aircraft damage/losses (and damage to buildings etc; and personal injury/death.
If there is an incident or accident it can involve law enforcement agencies, accident investigators, insurers and financiers/lessors, among others.
Personal injury law in aviation is based on tort, in common law jurisdictions, but internationally has evolved via a series of international treaties, such as the Warsaw Convention.
More broadly, international aviation is governed by the Chicago Convention and its annexes. The Chicago Convention is overseen by an agency of the United Nations, the International Civil Aviation Organisation (ICAO), which is based in Montreal, Canada.
Then each country has its own aviation laws, for example the USA (overseen mainly by the Federal Aviation Administration (FAA)). In Europe, the European Union created the European Aviation Safety Agency (EASA) to oversee collectively agreed air law. Each country has a regulator such as the FAA, CAA in the UK, and EASA – Europe is unusual in having EASA and individual regulators in each EU Members State. Some countries base their aviation laws closely on FAA or EASA, though almost all countries are signatories to ICAO and thus that is the basic reference to which civil aviation around the world adheres, in general.