Dashi can be made from konbu kelp, bonito flakes, niboshi (boiled then dried baby Japanese anchovies), dried shiitake mushrooms and more, used separately or in combination, depending on the depth and flavor you're aiming for. Most chefs and home cooks have their own "secret" recipe.
Nobody knows what ingredients were first used to make dashi, or when it was first thought up. But a cookbook written around the 15th century mentions both konbu seaweed and dried bonito flakes. By the second half of the 17th century, it appears to have become common to combine the two to make the most common type of dashi–ichiban-dashi, which is characterized by a delicate and subtle flavor and aroma. "Ichiban," which literally means "number one," tells you that this dashi comes from the first straining of the ingredients.
While konbu is rich in glutamate and bonito flakes are full of inosinic acid, combining them results in a synergy rather than a simple addition of flavors.
Reflecting Japan's long tradition of recycling, the second most popular form of dashi, niban-dashi, is made by extracting additional umami flavor from the konbu and bonito flakes used for ichiban-dashi ("niban" is "number two"). The intensity of flavor and fragrance is not as strong as that of ichiban-dashi, but this dashi is good enough for most dishes other than clear soups.