Archaeologists look at all past cultures, even those that are not usually thought of as "archaeological." Historic archaeology deals with sites and artifacts that date to the period of time when written records are also available. In Wisconsin this is after about 1700 A.D., but in some parts of the world such as Greece or the Middle East, written records have existed for thousands of years.
Written records would seem to eliminate the need for doing archaeological research with material remains. However, written records tell only part of the story about the past, and that story is often biased or idealized from one perspective (that of the recorder). Thus, most histories, even diaries and personal journals, often won't record such details as what people were eating, how they were preparing their food, what their lives were like. The archeology of historic sites provides powerful complementary information to that provided by written records, particularly for segments of a culture that didn't record their own history, such as peasant classes.
Even with good records available, the archaeological evidence might be able to correct misinformation or fill in many details.