The success of weed control is critical for our food security. Non-chemical weed control is a promising technique in sustainable agriculture to ensure the food security. In this review, multiple directed energy weed control methods are reviewed with a specific focus on laser and optical radiation weed control. The mechanisms of the weed control in terms of adverse ablation, radiation thermal effects, and molecular-level damages are systematically reviewed. In particular, the underlying mathematical models determining the dose and response relationship of the weed control are also analyzed for a rigorous study of the physical law of the control process. Challenges of applying the techniques into practice are also illustrated to guide practical weed control applications.