If it is a child seat approved by MLIT in Japan, FMVSS in the US, or UNECE in Europe, or a CARES device, you can use it on board. There are, however, some types of child seat that cannot be used even if they have been approved by the aforementioned standards.
Check here for more details.

Child seats that cannot be used on board should be checked in at the baggage counter.
Depending on the size of the child seat, in some cases, you may not be able to carry it on board. Check here for more details.