This article will be a quick overview of the different ways of composting. Since each has intricacies that can be expounded on this will not be a tutorial but rather a list of benefits and drawbacks of each as well as which is best suited to different situations.
When you start gardening you come to realize pretty quickly the immense value of compost, partly as a fertilizer but mostly as a means to maintain soil structure and composition. Compost is invaluable in returning organic material and microorganisms to soil that has been depleted from continued use. Almost everyone has something to compost, from kitchen scraps in an apartment, grass clippings and leaves from the lawn of a house, to manure and used animal bedding on a farm, and in each situation there is a way to decompose your “waste” material for reuse in your garden. So without further ado here is a short list of the different ways to decompose materials.
Compost Piles
This is what most people think about when they think of compost. Layers of greens (nitrogen) and browns 
(carbon) in a heap that gets turned every so often. Compost piles are best suited to open areas for a number of reasons. They take up space, attract flies, insects and critters, and it they are not turned often enough they will go anaerobic and begin to produce foul odors. They are however the best way to process large amounts of material and as a matter of fact are ineffective if they are too small because they cannot retain moisture or heat. The fact that they can be scaled from the size of a couple 1m3 bins all the 
way to windrows makes them great on farms or even houses with big yards. They do require some work to turn, (weekly is recommended) so that is something to take into account.
Tumblers
Tumblers decompose in the same way that compost piles do but they make the process of aeration much easier. They are great for a home that doesn’t produce large amounts of compostable material, or for 
someone who does not want to, or is incapable of turning a pile with a shovel. One thing to note is that they still have to have a correct ratio of greens and browns (about 30/1). If you just load these up with kitchen scraps they will putrefy no matter how much you turn them. If you don’t have a yard or a source of dry leaves to mix with your kitchen scraps you can shred and mix in cardboard to get you C/N balance right.
Bokashi
Bokashi is not technically composting it is actually a process of fermentation with lactic acid bacteria. It is done by mixing food scraps with bokashi powder or liquid lactobacillus serum and allowing them to 
ferment. The process takes about two weeks and doesn’t have a foul odor. Once fermented the material is not actually decomposed but will break down much faster (two weeks) when added to compost or directly to soil. From start to finish the process takes about a month which is half the time of a regularly turned compost pile and it ensures that your compost and soil are inoculated with the immensely beneficial lactobacillus bacteria. The reason I mention it here is because it works wonders when combined with the above and below systems, and I have personally had great results with it.
Vermiculture
Most people know that worm castings are one of the best fertilizers out there. They are an excellent source of humic and fulvic acids and contain myriad beneficial bacteria to boost the life in your soil as well as all the nutrients present in what you fed to your worms. What most people don’t know is how easy it is to keep a worm farm at home. Worms are great composters, will eat almost anything, and are great for someone with limited space. Worms can eat up to half their weight every day so a pound or two of worms can easily take care of all the kitchen waste a small family produces. Worm bins also have almost no odor and if set up right will not attract any other insects. Vermiculture can be scaled up to any size and it is well worth it for anyone who is serious about organic gardening to look into producing their own worm castings because of their immense value in growing healthy plants and having healthy soil.
Black Soldier Fly Larvae
BSF larvae are an interesting option for composting and are most useful to someone who also keeps 
chickens or fish because the larvae can be harvested and used as high protein feed. BSF do not spread disease because they spend most of their lives in their larval stage. As flies they don’t have mouths and only live for long enough to reproduce. The effluent produced from their digestive process can also be diluted and used as fertilizer. These systems can be smelly though and are not well suited to enclosed spaces.
Cockroach Composts
Yes, I know, GROSS! But it is worth mentioning that cockroaches are also excellent composters and many people have had great success using them. I personally have no experience with this method of composting nor do I have any immediate plans to acquire any. It is however a method of composting and as such belongs in the list.
Anaerobic Compost
I have heard some good things about anaerobic composting and I have also heard some bad. Anaerobic compost is smelly and takes quite a bit longer than aerobic composting. It is said that anaerobes can break down organic matter into a wider spectrum of minerals and nutrients but it is also worth considering that 
many important elements such as nitrogen tend to be converted into gases and to dissipate. The only experience I have with this method of composting has been with bio-gas digesters and that experience has been positive. However it is worth it to note that biodigesters can be somewhat complex systems that require cleaning and maintenance and may not be suited to the average organic gardener.
Well that concludes my list and I’m sure there are some systems that I have overlooked and as I continue to learn I will amend this post. Like I said this was just a quick overview and I will be expounding on the different ways to do each of these properly in different posts. If I were to make one recommendation for any compost system it would be to incorporate Lactobacillus serum. It speeds up the process, reduces odors, converts nutrients into plant available forms, and enhances soil vitality. I hope this info has been useful to you and if you want to learn more about a specific type of composting check out the Composting category of posts here on this site.