A decade before Michaelis and Menten, Victor Henri found that enzyme reactions could be explained by assuming a binding interaction between the enzyme and the substrate. His work was taken up by Michaelis and Menten, who investigated the kinetics of invertase, an enzyme that catalyzes the hydrolysis of sucrose into glucose and fructose. In 1913 they proposed a mathematical model of the reaction. It involves an enzyme E binding to a substrate A to form a complex EA that releases a product P regenerating the original form of the enzyme. This may be represented schematically as
where  (forward rate constant),  (reverse rate constant), and  (catalytic rate constant) denote the rate constants, the double arrows between A (substrate) and EA (enzyme-substrate complex) represent the fact that enzyme-substrate binding is a reversible process, and the single forward arrow represents the formation of P (product).
Under certain assumptions – such as the enzyme concentration being much less than the substrate concentration – the rate of product formation is given by
in which  is the initial enzyme concentration. The reaction order depends on the relative size of the two terms in the denominator. At low substrate concentration , so that the rate  varies linearly with substrate concentration  (first-order kinetics in ). However at higher , with , the reaction approaches independence of  (zero-order kinetics in ), asymptotically approaching the limiting rate . This rate, which is never attained, refers to the hypothetical case in which all enzyme molecules are bound to substrate. , known as the turnover number or catalytic constant, normally expressed in s , is the limiting number of substrate molecules converted to product per enzyme molecule per unit of time. Further addition of substrate would not increase the rate, and the enzyme is said to be saturated.
The Michaelis constant  is not affected by the concentration or purity of an enzyme. Its value depends both on the identity of the enzyme and that of the substrate, as well as conditions such as temperature and pH.
The model is used in a variety of biochemical situations other than enzyme-substrate interaction, including antigen–antibody binding, DNA–DNA hybridization, and protein–protein interaction. It can be used to characterize a generic biochemical reaction, in the same way that the Langmuir equation can be used to model generic adsorption of biomolecular species. When an empirical equation of this form is applied to microbial growth, it is sometimes called a Monod equation.
Michaelis–Menten kinetics have also been applied to a variety of topics outside of biochemical reactions, including alveolar clearance of dusts, the richness of species pools, clearance of blood alcohol, the photosynthesis-irradiance relationship, and bacterial phage infection.
The equation can also be used to describe the relationship between ion channel conductivity and ligand concentration, and also, for example, to limiting nutrients and phytoplankton growth in the global ocean.