Since Klaytn supports Ethereum’s EVM, ERC-20 and ERC-721 solidity code can be directly executed on Klaytn without modification. However, if your code has any external dependency such as Provable, Oraclize, Chainlink, etc., it cannot be executed on Klaytn.
Additionally, Klaytn is trying to define token standards through KIP (GitHub - klaytn/kips: Website).