Green and red macroalgae are closely related organisms, and with terrestrial plants, and constitute the base of marine food webs in coastal ecosystems. Green and red seaweeds, as all living organisms, require essential metals, such as copper, iron, zinc, which can act as co-factors for several proteins and enzymes; however, these metals in excess can induce stress and impair cell viability. Most important negative effects of metal excess are related to the induction of an oxidative stress condition, characterized by the over-accumulation of Reactive Oxygen Species (ROS). In this respect, copper, abundant in wastewaters disposed to coastal environments from domestic and industrial activities, has been one of the most studied metals. Different investigations have provided evidence that green and red macroalgae display several defenses against copper excess to prevent, or at least reduce, stress and damage, among which are cellular exclusion mechanisms, synthesis of metal-chelating compounds, and the activation of the antioxidant system. Most important defense mechanisms identified in green and red seaweed involve: metal-binding to cell wall and epibionts; syntheses of metallothioneins and phytochelatins that accumulate in the cytoplasm; and the increase in the activity of antioxidant enzymes such as superoxide dismutase, ascorbate peroxidase, glutathione peroxidase and catalase, and greater production of antioxidant metabolites as glutathione and ascorbate in organelles and the cytoplasm. In this review, we go through historical records, latest advances, and pending tasks aiming to expand our current knowledge on defense mechanisms to copper excess in green and red macroalgae, with emphasis on biochemical and molecular aspects.