Everyone knows that the varroa mite and pesticides/fungicides are the major problems to successfully maintaining a healthy hive. There is little an individual beekeeper can do in regards to agriculturally applied pesticides and fungicides. However, the beekeeper can take action against varroa. The traditional approach has been to control the varroa mite using chemical treatments. This method has had short term success, but the mites have developed resistance to these treatments. An alternate approach is to improve the genetics of your bees so that they can naturally counter the varroa mite. Some bees have developed traits whereby some worker bees remove brood infected with varroa and thus slow or stop the growth of the varroa infestation. This behavior has been given the name of "Varroa Sensitive Hygiene or VSH". Some bees exhibit this trait naturally; such as the Primorski Russian bees. Other bee sub-species have gained this trait through selective breeding. VSH Italian, VSH Carniolans and Minnesota Hygienic queens are all commercially available.
A good description of the Varroa Sensitive Hygiene trait is summarized at the following link.
VSH bees are not yet widely used. Most, if not all, queen bees in spring time bee packages are NOT of the VSH variety. To get this trait the beekeeper must personnally procure and introduce VSH queens into their apiary. VSH queen bees tend to be slightly more expensive ($5 to $10) than non-VSH bees.