Just as in the United States, parents are eligible for the child tax credit. Be aware that similar rules apply: You must support your child, and he or she must live at home with you.
The planning quirk for American parents abroad is that they have to make a choice.
They can opt for the child tax credit, which reduces tax liability dollar for dollar, as well as the additional child tax credit if the filer gets less than the full $1,000 per kid as part of the child tax credit.
Alternatively, taxpayers can take the foreign earned income exclusion, which permits expats to exclude some of the income they've earned abroad. For the 2016 tax year, you can exclude a maximum of $101,300.
You cannot have both the child tax credit and the foreign income exclusion because of recent legislation.
Whether it makes sense to take one or the other will depend on your circumstances and the tax regime of the nation in which you're living.