Not every spot is the same spot
This is the most important thing to understand before starting, because it determines both the treatment and the expectation. Under the word pigmentation hide several completely different conditions that look similar at first glance.
Sun spots and age spots are the direct result of accumulated exposure over years. They usually sit in the relatively upper layers of the skin, so they respond comparatively well to treatment.
Marks left after a spot or inflammation are a different story: they tend to fade on their own over months, and treatment mainly speeds up the process and prevents it getting worse.
Melasma, symmetrical patches that usually appear on the cheeks, forehead and above the lip, may be linked to hormonal changes, pregnancy and the pill. It tends to return and calls for more cautious expectations, and sometimes medical consultation as well.