Recent modifications have been made to generalize the Embedded Atom Method (EAM) to describe bonding in diverse materials. By including angular dependence of the electron density in an empirical way, the Modified Embedded Atom Method (MEAM) has been able to reproduce the basic energetic and structural properties of 45 elements. This method is ideal for examining interfacial behavior of dissimilar materials. This paper explains in detail the derivation of the method, shows how parameters of MEAM are determined directly from experiment or first principles calculations, and examine the quality of the reproduction of the database. Materials with fcc, bcc, hcp, and diamond cubic crystal structure are discussed. A few simple examples of the application of the MEAM to surfaces and interfaces are presented. Calculations of pullout of a SiC fiber in a diamond matrix as a function of applied stress show nonuniform deformation of the fiber.