What is the most of the more important civil and criminal cases are heard in?

Most criminal cases are heard in the state trial courts.

By comparison, the federal courts hear relatively few criminal cases (only 78,428 in 2010), many related to illegal Immigration, whereas the state courts, combined, try more than a million criminal cases per year.

A report published by the Bureau of Judicial Statistics estimated 1,132,290 criminal cases were filed in state courts in 2006 (the most recent year for which aggregate statistics are available).