The term antiaromaticity was first proposed by Ronald Breslow in 1967 as "a situation in which a cyclic delocalisation of electrons is destabilising". The IUPAC criteria for antiaromaticity are as follows:
#The molecule must be cyclic.
#The molecule must be planar.
#The molecule must have a complete conjugated π-electron system within the ring.
#The molecule must have 4n π-electrons where n is any integer within the conjugated π-system.
This differs from aromaticity only in the fourth criterion: aromatic molecules have 4n +2 π-electrons in the conjugated π system and therefore follow Hückel’s rule. Non-aromatic molecules are either noncyclic, nonplanar, or do not have a complete conjugated π system within the ring.
Having a planar ring system is essential for maximizing the overlap between the p orbitals which make up the conjugated π system. This explains why being a planar, cyclic molecule is a key characteristic of both aromatic and antiaromatic molecules. However, in reality, it is difficult to determine whether or not a molecule is completely conjugated simply by looking at its structure: sometimes molecules can distort in order to relieve strain and this distortion has the potential to disrupt the conjugation. Thus, additional efforts must be taken in order to determine whether or not a certain molecule is genuinely antiaromatic.
An antiaromatic compound may demonstrate its antiaromaticity both kinetically and thermodynamically. As will be discussed later, antiaromatic compounds experience exceptionally high chemical reactivity (being highly reactive is not “indicative” of an antiaromatic compound, it merely suggests that the compound could be antiaromatic). An antiaromatic compound may also be recognized thermodynamically by measuring the energy of the cyclic conjugated π electron system. In an antiaromatic compound, the amount of conjugation energy in the molecule will be significantly higher than in an appropriate reference compound.
In reality, it is recommended that one analyze the structure of a potentially antiaromatic compound extensively before declaring that it is indeed antiaromatic. If an experimentally determined structure of the molecule in question does not exist, a computational analysis must be performed. The potential energy of the molecule should be probed for various geometries in order to assess any distortion from a symmetric planar conformation. 
This procedure is recommended because there have been multiple instances in the past where molecules which appear to be antiaromatic on paper turn out to be not truly so in actuality. The most famous (and heavily debated) of these molecules is cyclobutadiene, as is discussed later.
Examples of antiaromatic compounds are pentalene (A), biphenylene (B), cyclopentadienyl cation (C). The prototypical example of antiaromaticity, cyclobutadiene, is the subject of debate, with some scientists arguing that antiaromaticity is not a major factor contributing to its destabilization. Cyclooctatetraene appears at first glance to be antiaromatic, but is an excellent example of a molecule adopting a non-planar geometry to avoid the destabilization that results from antiaromaticity. Because antiaromatic compounds are often short-lived and difficult to work with experimentally, antiaromatic destabilization energy is often modeled by simulation rather than by experimentation.