Travertine can be washed with fiber brushes, mild soap or detergent, and water. In extreme cases, Travertine can be cleaned with a light spray of a pressure washer, in which case the Travertine may need to be resealed.

For wine spills or tough stains that need extra work, consider a Poultice Powder.

There are also several cleaners on the market that are aimed specifically at Travertine:

DuPont™ StoneTech® Professional Revitalizer Cleaner and Protector: http://amzn.to/1lROONJ