STEP-BY-STEP ANSWER:
Step 1: Identify that alkylating agents work by attaching alkyl groups to DNA strands.
Step 2: Understand that this attachment causes DNA cross-linking or breaks which inhibit DNA replication.
Step 3: Recognize that impaired DNA replication leads to cell death, particularly in rapidly dividing cancer cells.
Step 4: Acknowledge that this mechanism forms the basis of their use in chemotherapy.
Final Answer: Alkylating agents cause DNA damage by adding alkyl groups, leading to cross-linking or strand breaks, which inhibit cancer cell replication and promote cell death.