At least in the US, they almost always involve a custody fight.

(A divorced parent actually kidnapped their own kid, or is late dropping a kid off.). Less commonly, it will involve other family members. (A parent is a drug addict, so the grandparents/uncle take the kid.)

In a vanishingly rare subset of the alerts, it is a kidnapping where a kid is taken by a stranger.

The phone settings are usually called "emergency alerts" or similar.

It's a US-specific system for alerting people to missing children. It's named after Amber Hagerman⁰, a 9-year-old who was abducted and murdered in the '90s. On smartphones they can appear as (very loud) notifications with details about the missing child, potential abductors, vehicle, etc. You'll also see the same info on electronic message boards along the motorway.

[0] https://en.wikipedia.org/wiki/Amber_alert#Namesake

It's when you destroy the attention span of anyone within driving distance of a custodial dispute.

There's also silver alerts, where you do the same for a missing old person.

As I understand it's called "Child Rescue Alert" in the UK.

An Amber alert is an alert sent out by the local authorities in the US to all smartphones (and maybe radio? I'm too young to use a radio often) when a child is missing / suspected to be abducted.

A Silver alert is very similar and is sent out when an elderly person (esp. with memory issues) is missing.

The default tone on iOS is a cross between a smoke detector and a baby crying.

It's system to ask the public for help in finding abducted children.

https://en.wikipedia.org/wiki/Amber_alert