What you learned in school
Biology textbooks taught that deoxygenated blood in veins was blue until it contacted oxygen and turned red. Students learned to identify "blue blood" in diagrams showing the circulatory system. This explained why veins appear blue through the skin, and medical textbooks included illustrations of blue veins versus red arteries.
What we know now
Students were taught that deoxygenated blood in veins is blue, and only turns red when exposed to oxygen. This explained why veins appear blue through the skin. Textbooks often included diagrams showing blue veins and red arteries. In reality, blood is always red - it's just darker when deoxygenated. Veins appear blue due to the way light penetrates skin and is absorbed and reflected. Blue light penetrates deeper than red light, making the veins appear blue to our eyes. This is purely an optical phenomenon.