Ivanov, Kuznetsov and Smirnov are some of the most common family names in Russia. Russian surnames are loosely grouped into four main categories: patronymic, geographical, descriptive and occupational. Kuznetsov, for example, means "blacksmith," and it is almost as common among Russian-speaking people as the equivalent, Smith, is in English.
Ivanov is an example of a patronymic surname. It is derived from the very common Russian first name Ivan, which means "God's grace" and is often treated as the equivalent of the English name John. "Ivanov," therefore, is roughly equal to "Johnson." Popov is a common trade name. Like Kuznetsov, it refers to the father's profession, which in the case of "Popov" is that of a priest, or "pope."
Descriptive Russian surnames often refer to concepts, geographical features and animals. Volkov, for example, is derived from the Russian word "volk," which means "wolf." Morozov is derived from the Russian term for extreme cold. Geographical surnames are often straight transliterations of a city or village name, though sometimes they are altered with a modifying suffix to indicate the terms' use as names. Thus, Smolensky generally refers to a family from Smolensk, and Riazanov is a common name for families that are associated with Ryazan.