In recent years, the field of covalent kinase drug discovery has been rapidly evolving. Several covalent kinase inhibitors (such as afatinib, osimertinib, ibrutinib and acalabrutinib) have obtained market approval or are currently in early and advanced clinical studies. Both covalent irreversible and covalent reversible kinase inhibitors have been discovered, providing an opportunity to target specific kinases, mutations and or pharmacokinetic (PK)/pharmacodynamic (PD) profiles. This chapter will give an overview of the state-of-the-art of covalent kinase drug discovery. First, the concept of covalent enzyme inhibition will be introduced and a comparison to non-covalent inhibitors will be made, highlighting possible advantages and disadvantages of such mechanisms of action (MOA). The importance of selectivity, drug-target residence times and inhibitor kinetics will also be discussed. Finally, a literature overview of irreversible and reversible covalent kinase inhibitors that are currently on the market or in the clinical testing phase will be presented.