In socially monogamous species pair partners often form and maintain long-term pair-bonds. Relationships between pair partners are dynamic and driven by both cooperation and conflicts between the sexes. Successful reproduction depends on behavioural coordination and cooperation, which includes continuing mutual responsiveness between the pair partners, as well as conflicts, for example, over parental investment. Gonadal hormones, such as testosterone, centrally regulate reproduction and are potentially involved in the formation and maintenance of pair-bonds. In greylag geese (Anser anser), a positive within-pair testosterone co-variation (TC) among pair partners has been observed at the seasonal level. Goose pairs with a higher TC have a higher reproductive output and long-term success than pairs with lower TC, but it is still not clear whether TC is cause or consequence. In this article, I (i) summarize the evidence for hormonal partner compatibility in geese, (ii) ask whether TC is restricted to monogamous and biparental systems and (iii) synthesize open questions or new aspects of information we may draw by studying hormonal partner compatibility. From longitudinal studies in geese, we know that TC decreases with pair-bond duration. This indicates some form of ‘attritional effect’ over the years rather than an improved breeding performance with increasing familiarity between the partners (the ‘mate familiarity hypothesis’). Under certain circumstances, for example, during ageing, selection may not act in the same direction for males and females. Partner preference increased female androgen levels during laying and social instability may impinge on the pair's TC. Data from other species show that TC is not restricted to monogamous species, but presumably the link between TC and reproductive output may be primarily relevant in species with biparental care. This article surveys the major unanswered questions relating to hormonal partner compatibility and previews potential future work for addressing those open issues.