Cyclobutadiene is a classic textbook example of an antiaromatic compound. It is conventionally understood to be planar, cyclic, and have 4 π electrons (4n for n=1) in a conjugated system.
However, it has long been questioned if cyclobutadiene is genuinely antiaromatic and recent discoveries have suggested that it may not be.  Cyclobutadiene is particularly destabilized and this was originally attributed to antiaromaticity. However, cyclobutadiene adopts more double bond character in two of its parallel bonds than others and the π electrons are not delocalized between the two double-bond-like bonds, giving it a rectangular shape as opposed to a regular square. As such, cyclobutadiene behaves like two discrete alkenes joined by two single bonds, and is therefore non-aromatic rather than antiaromatic.
Despite the lack of this π-antiaromatic destabilization effect, none of its 4n π-electron relatives (cyclooctatetraene, etc.) had even close to as much destabilization, suggesting there was something more going on in the case of cyclobutadiene. It was found that a combination of angle strain, torsional strain, and Pauli repulsion leads to the extreme destabilization experienced in this molecule.
This discovery is awkward in that it contradicts basic teachings of antiaromaticity. At this point of time, it is presumed that cyclobutadiene will continue to be used to introduce the concept of antiaromaticity in textbooks as a matter of convenience, even though classifying it as antiaromatic technically may not be accurate.