1. This is the one area that hobbyist can spend the most effort on. Higher levels of nitrates and phosphates can lead to problems such as nuisance algae growth or even stressing your fish and/or corals if the levels get high enough. There are a few different ways you can do this.  Live rock, Algae scrubbers, macro algae, Carbon dosing, water changes, Deep Sand Beds, and Refugiums.
     
  2. Live rock will not only hold the bacteria that processes ammonia and nitrites, but it will also hold bacteria that also eats nitrates and converts nitrogen into a nitrogen gas which is released into the atmosphere.  This is one of the more natural ways to reduce the nitrates produced by your set-up.
     
  3. Algae scrubbers are designed to hold/grow algae allowing this algae growth to naturally remove nitrates and phosphates from the water.  You are basically using I flow and high levels of lower spectrum lighting to grow algae.  Although an algae scrubber can also provide some biological filtration, their primary benefit is the removal of nitrates and phosphates. This too is a very safe and proven way to remove both nitrates and phosphate from your set-up.  You can find some more details about algae scrubbers in the following link.  Some research suggests that one of the benefits of algae in your tank is that the algae can consume / filter out some unwanted trace elements out of the water (like you would expect from chemical filtration).  The algae also provides a food source for most pods will also put some good trace elements back into the water.
     
  4. Macro algae grown in your set-up can remove a lot of nitrates and phosphates from the water.  Although a macro algae can also provide some biological filtration, their primary benefit is the removal of nitrates and phosphates.  This is a very common approach for many hobbyist to use macro algae, like cheato ( the common name for Chaetomorpha algae), in a sump or refugium.  Growing mangroves in your set-up is also said to work just as well as macro algae, but I have no firsthand experience with it. I have obtained really good results with a few different types of macro algae grown in a sump.
     
  5. Carbon Dosing can also be very effective; however, it is not a good fit for most people who are new to the hobby.  I had tried a few different approaches to carbon dosing and found it to have great results pretty fast as well.  I now prefer to use more natural methods to removing nitrates and phosphates from my marine aquariums. The below link will give you a little more information about carbon dosing should you like to know more.  There are some real risks to carbon dosing so make sure you do your homework first before trying it.  I had stopped carbon dosing some time ago in favor of more natural methods that are a lot less risk to your set-up.
     
  6. Deep Sand Beds I never have never actually tried this approach as I have never needed to explore other methods of removing nitrates / phosphates from the water.
     
  7. Refugiums can also be an effective means to remove nitrates and phosphates from your set-up.  Although this really is not a unique form of nutrient removal, but it does allow you to include a combination of some of the above mentioned methods in a partially enclosed environment.  The more commonly found approaches used include: deep sand beds, live rock, and macro algae.  This can be set-up as a compartment in your sump, or as a separate tank/container plumbed into your set-up.
     
  8. One of the simple and easiest ways to reduce nitrates and phosphates in aquarium still remains to complete a water change.  An adequately maintained marine aquarium with a good weekly water change routine should have minimal nitrates and phosphates in the water.