Which method(s) of cellular transport require energy? Which method(s) do not?
In the ones which do not require energy, there is movement of substances down the concentration gradient. If there is steepness in the potential difference of any substance like water or even CO2, O2 and small molecules, the move by diffusion without needing energy.
Where as in the active transport, things have to be done forcefully. Like transporting a substance from region of lower concentration to higher concentration which is not likely to occur itself so it requires energy.This is done against the concentration gradient. Like phagocytosis, where bacterias are engulfed. Also the releasing of enzymes require ATP. Some pumps like carrier protein of NA+ K+ pump also requires energy.