April 29, 2010
      
                  
        
  Author(s)
  Chin P. Cheng,   R  Grimm,   Paul S. Julienne,   Eite  Tiesinga
 
       
            
    
    
        Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found manifold experimental applications, opening up the way to important breakthroughs. This Review gives a broad coverage of the