The magic that is cheese only really needs four ingredients to happen: milk, salt, rennet (or some other coagulant, as I discussed earlier), and microbes. Like everyone, I used to be vaguely aware that there were "good" bacteria and molds that grew on and in cheese, and that's where my interest ended. But there's a real variety of microbes that bring us the variety of cheeses we enjoy, and they're worth knowing about. I would be a bad scientist if I didn't mention that, since I am no microbiologist, if you want all the details, you should peruse the Wikipedia articles I'll link to or consult your local library.
Many modern cheeses are made with preselected cultures, consisting of only a few types of microbe, but many traditional cheeses are inoculated using whey or other products from previous batches, meaning that they can be made with dozens of types of microbe, some highly unusual. This microbial wealth is among the many reasons that traditional cheeses can be so much more complex than modern, controlled-inoculation cheeses. Modern microbiology has yet to fully explain the role of all microbes in cheese-flavor and cheese-ripening, so the limited selection of controlled inoculation produces cheeses that may be less interesting.
Lactic Acid Bacteria
Lactic acid bacteria are often called "starter cultures", as they play the main role in converting the basic milk sugar, lactose, into lactic acid, a step which lowers cheese pH and makes the cheese inhospitable to many spoilage organisms and is the first step towards deliciousness. There are essentially two main families of lactic acid bacteria: lactococci (sphere-shaped, lactic-acid producing bacteria) and lactobacilli (rod-shaped, lactic-acid producing bacteria). Streptococci can also play an important role in initial cheese ripening, and are very important in yogurt-making. Although many of these bacteria die off after the initial step of cheesemaking, there are varieties that survive and continue to contribute to cheese flavor in many cheeses, especially alpine (Emmental, Gruyere, etc) and Italian hard (Grana Padana, Pecorino Romano, etc) cheeses.
Propionic Acid Bacteria
These bacteria, and specifically Propionobacter shermanii, are able to digest acetic acid and convert it to sharp, sweaty-smelling propionic acid and carbon dioxide. The carbon dioxide is what gives Emmental and other Swiss cheeses their characteristic "holes", and the propionic acid contributes to their complex, especially sharp bouquet. Interestingly, several species of propionibacteria inhabit human skin, and help produce "unwashed" odors.
Molds (Blue and White)
Molds love cheese. Leave any cheese in a fridge without protection and it will quickly be colonized by a fuzzy carpet of interestingly colored spores. Most of the molds that grow on cheese are species of Penicillium, but some cheeses, like St. Nectaire, develop all kinds of crazy surface molds, most of which are not harmful and in fact contribute to that cheese's unique flavor. Only two species of blue mold, P. roqueforti and P. glaucum, give rise to the unique flavor and texture of the hundreds of blue cheese which are revered throughout the world. These blue molds are capable of growing in remarkably low-oxygen environments, which makes them perfectly suited for the small cracks in the interior of a ripening cheese. In fact, cheesemakers regularly pierce and inoculate channels through to-be-blued cheeses in order to encourage the growth of these molds. Blues, like Roquefort, Stilton, Gorgonzola, and Cabrales are some of the most famous cheeses in the world, but blue molds also frequently grow on the surface of goat cheeses, adding color and flavor, but without growing in the interior, as is the case of the unsurpassable Monte Enebro.
White molds, which are found on the outside of all types of soft-ripened cheeses, are subspecies of P. camembertii (also called P. candidum). These white molds produce enzymes that break down the milk proteins of the curds, leading to the characteristic ripened layer surrounding a firm interior in many of these cheeses. The flavor compounds that are produced by this enzymatic breakdown are generally garlicky or earthy; unfortunately, ammonia is also a by-product of this breakdown, and so it is advisable to let these cheeses breathe (sit uncovered) in order to allow the highly volatile ammonia to dissipate.
Last but perhaps most notorious are the smear bacteria, which are responsible for the room-clearing ability of Epoisses, Münster, and Limburger. These smear bacteria are officially known as Brevibacter linens. They can't live in acidic or deoxygenated environments, and so cannot survive in the interior of cheeses. Since they need salty (up to 15%), moist environments to grow, they must be encouraged to do so by continual washing or wiping of the cheese surfaces, a process which results in the development of the characteristic red "smear" surface of so-called "washed-rind" cheeses. B. linens excels at breaking down proteins into, well, stinky odor compounds, producing oniony or garlicky, fishy, and sweaty aromas. Some cheeses, like the great alpine cheeses, are wiped only during part of their ripening, producing a muted complexity of flavor, rather than the nasal assault that accompanies many cheeses that play host to B. linens. The aroma of the washed-rind cheeses is often compared to smelly feet by both fans and detractors, a fact which is easily understood, as brevibacter are ubiquitous on human skin, and grow especially well without interference from personal hygiene.
So, next time you pick up a piece of cheese, think of the huge microbial society that's gone to the trouble of producing the masterpiece in front of you. Then you can pretend you're Godzilla or something when you eat the cheese, with thousands of screaming microbes fleeing for the escape capsules. At least, that's what I do.