Calculus has many applications in fields like engineering, science, economics, and more. It is used to model rates of change and optimize solutions. Some examples given include using calculus in building skyscrapers and bridges, modeling drug concentrations in the body, measuring growth rates in biology, and developing better navigation systems. Calculus underlies concepts in physics like motion and gravitation. It is also used in fields like business, medicine, mapping, and solving paradoxes.