The International Criminal Court has issued an arrest warrant for Vladimir Putin for war crimes related to the abduction of thousands of children from Ukraine and their removal to Russia. The most immediate implication is that Putin will be unable to travel to ICC member states without risk of being arrested. Russia does not recognize the ICC, so Putin would not face arrest there. The ICC also issued a warrant for the arrest of Maria Lvova-Belova, the commissioner for Children’s Rights in the Office of the President of the Russian Federation, for her involvement in the abductions.
Some excellent analysis of the implications of this indictment has come out since the arrest warrants were issued. Take a look:
"How the ICC's Warrant for Putin Could Impact the Ukraine War" - United States Institute for Peace
https://www.usip.org/publications/2023/03/how-iccs-warrant-putin-could-impact-ukraine-war
"How Will the ICC's Arrest Warrant for Putin Play Out in Practice?" - Just Security
"The ICC Goes Straight to the Top: Arrest Warrant Issued for Putin" - Just Security
https://www.justsecurity.org/85529/the-icc-goes-straight-to-the-top-arrest-warrant-issued-for-putin/
Official ICC Statement on the Arrest Warrants:
