Boxers as a dog breed are relatively young. The first boxers didn't appear until the late 1800's and were originally bred to be hunting dogs for use in the hunting of wild boars, deer, and even bears. For such a young breed of dogs, however, the boxer is known for its exceptional breeding and the beautiful shades that appear in their coats. There is actually a fairly exact science that goes into the breeding of various bloodlines of boxers in order to achieve the coloring and markings that are familiar to most boxer lovers.
Though boxers may show a variety of different markings, there are actually only two recognized coat colors that appear on these dogs. The first, known as fawn, can range in shade from a light tan to a darker and more red mahogany color. The second coat color, known as brindle, features a striped pattern with black stripes covering a base color of fawn. The stripes on a brindle boxer can be so thick that the fawn color nearly disappears altogether, resulting in what are commonly called reverse or black brindles; even if the dog appears almost entirely black it is still a brindle however, as pure boxers lack a gene which would allow for a true black coat.
Breeders use great care when choosing boxers to breed together, as the fawn and brindle colorings of their coats are passed on genetically and through careful tracking of bloodlines it's possible to predict more or less what the coats of the offspring will look like. Brindle coats are the result of a dominant gene, so if it's present at all then the dog will feature a brindle pattern. This doesn't mean that every dog with a brindle coat will have only brindle puppies, however; if a dog with a dominant brindle gene and a recessive fawn gene is mated with another dog that features the same dominant and recessive genes then there is a 25% chance that each puppy will be fawn and a 75% chance that it will be brindle. A fawn dog mated with another fawn will produce only fawn puppies, and a dog with two brindle genes (known as a double brindle) will produce brindle pups regardless of whether it is mated with a fawn or a brindle.
There are some cases where other coats appear, most notably in the case of white boxers who feature neither a fawn nor brindle coat. White boxers appear when genes are passed on from each parent that results in the offspring lacking the pigment needed for a fawn or brindle coat. Unfortunately these dogs also have a much higher chance of being deaf or suffering from other health problems due to these genetics as well. It is for this reason that most boxer organizations and a good number of breeders refuse to breed white boxers with others and recommend white boxers for pets only.