Self-assembled monolayers (SAMs) represent an important tool in context of nanofabrication and molecular engineering of surfaces and interfaces. The properties of functional SAMs depend not only on the character of the tail groups at the SAM-ambient interface, but are also largely defined by their structure. In its turn, the latter parameter results from a complex interplay of the structural forces and a variety of other factors, including so called odd-even effects, viz. dependence of the SAM structure and properties on the parity of the number (odd or even) of individual building blocks in the backbone of the SAM constituents. The most impressive manifestation of the odd-even effects is the structure of aryl-substituted alkanethiolate SAMs on Au(111) and Ag(111), in which, in spite of the fact that the intermolecular interaction is mostly determined by the aryl part of the monolayers, one observes a pronounced dependence of molecular inclination and, consequently, the packing density of the SAM-forming molecules on the parity of number of methylene units in the alkyl linker. Here we review the properties of the above systems as well as address fundamental reasons behind the odd-even effects, including the existence of a so-called bending potential, which is frequently disregarded in analysis of the structure-building forces. The generality of the odd-even effects in SAMs is additionally supported by the recent data for SAMs on GaAs, scanning tunneling microscopy data for SAMs on Ag(111), and the data for the monolayers with selenolate and carboxyl anchoring groups on Au(111) and Ag(111). The implications of these effects in terms of the control over the packing density and orientation of the tail groups at the SAM-ambient interface, structural perfection, polymorphism, temperature-driven phase transitions, and SAM stability toward such factors as ionizing radiation, exchange reaction, and electrochemical desorption are discussed. These implications place the odd-even effects as an important tool for the design of functional SAMs in context of specific applications.