As studied mainly on cisplatin, but presumably for other members as well, platinum-based antineoplastic agents cause crosslinking of DNA as monoadduct, interstrand crosslinks, intrastrand crosslinks or DNA protein crosslinks. Mostly they act on the adjacent N-7 position of guanine, forming a 1, 2 intrastrand crosslink.  The resultant crosslinking inhibits DNA repair and/or DNA synthesis. This mechanism leads to specific patterns of damage in DNA, which can kill cancer cells but can also increase the risk of secondary tumors developing.
Platinum-based antineoplastic agents are sometimes described as "alkylating-like" due to similar effects as alkylating antineoplastic agents, although they do not have an alkyl group.