β-lactam antibiotics are the most successful and commonly used antibacterial agents, but the emergence of resistance to these drugs has become a global health threat. The expression of β-lactamase enzymes produced by pathogens, which hydrolyze the amide bond of the β-lactam ring, is the major mechanism for bacterial resistance to β-lactams. In particular, among class A, B, C and D β-lactamases, metallo-β-lactamases (MBLs, class B β-lactamases) are considered crucial contributors to resistance in gram-negative bacteria. To combat β-lactamase-mediated resistance, great efforts have been made to develop β-lactamase inhibitors that restore the activity of β-lactams. Some β-lactamase inhibitors, such as diazabicyclooctanes (DBOs) and boronic acid derivatives, have also been approved by the FDA. Inhibitors used in the clinic can inactivate mostly serine-β-lactamases (SBLs, class A, C, and D β-lactamases) but have not been effective against MBLs until now. In order to develop new inhibitors particularly for MBLs, various attempts have been suggested. Based on structural and mechanical studies of MBL enzymes, several MBL inhibitor candidates, including taniborbactam in phase 3 and xeruborbactam in phase 1, have been introduced in recent years. However, designing potent inhibitors that are effective against all subclasses of MBLs is still extremely challenging. This review summarizes not only the types of β-lactamase and mechanisms by which β-lactam antibiotics are inactivated, but also the research finding on β-lactamase inhibitors targeting these enzymes. These detailed information on β-lactamases and their inhibitors could give valuable information for novel β-lactamase inhibitors design.