The evolutionary history of nearly all flowering plants includes a polyploidization event. Homologous genes resulting from allopolyploidy are commonly referred to as 'homoeologs', although this term has not always been used precisely or consistently in the literature. With several allopolyploid genome sequencing projects under way, there is a pressing need for computational methods for homoeology inference. Here we review the definition of homoeology in historical and modern contexts and propose a precise and testable definition highlighting the connection between homoeologs and orthologs. In the second part, we survey experimental and computational methods of homoeolog inference, considering the strengths and limitations of each approach. Establishing a precise and evolutionarily meaningful definition of homoeology is essential for understanding the evolutionary consequences of polyploidization.