Calcium This is vital to the health and growth of hard corals, coralline algae and many soft corals (who often have calcium spiracles within their tissues to stiffen their body mass and allow them to stand up in current).
Magnesium Unless your setup has a good Magnesium level you will find it impossible to achieve a good, constant, bio-available calcium and buffer level. Do use a good test kit as well as a high quality additive for Magnesium.
Strontium If you add Calcium to your set up you should also add Strontium. If you are not getting the coral and coralline algae growth you are looking for, despite a good calcium level, a lack of Strontium could well be the reason.
Trace Elements There are many trace elements in natural sea water - they are all, in one form or another important to marine life, yet many of them are impossible to test for. The easiest solution is to add a good combined trace element supplement on a weekly basis to make sure that all essential elements are present.
Vitamins In nature most fish and invertebrates eat a very varied diet with up to 150 different food organisms being included. In the aquarium this just isn't possible so it becomes necessary to make up the 'nutrition gap' with a good vitamin and amino acid supplement.
Minerals The very pure RO water that many marine keepers favour for their aquariums is very lacking in important minerals that form the basis of marine life in natural sea water - utilising a good mineral supplement will correct the mineral balance without contaminating the aquarium the way tap water would.
Coral Food Many corals photosynthesise in order to gain a portion of their food requirements, some need to catch all their food while many do a bit of both. The marine aquarist only has to look at the common branched coral forms, both hard and soft ,to see that many corals have evolved to actively catch various plankton organisms as a food source. Sadly, aquariums are incapable of supporting shoals of plankton so a high quality coral food or two will make an effective substitute. Your corals will look much better and grow faster.
Buffer Keeping a good alkali reserve will vastly increase the Ph stability of your set up while increasing the bio-availability of calcium and other trace elements. Your whole set up will benefit from a good stable Ph while you will find you don't have to test as much - decreasing your own aquatic stress levels!! Establish your set up's alkali reserve using a good alkalinity test kit, NOT ph the two are related but very different.