The objectives in the field of comparative cognition are clear; efforts are devoted to revealing the selection pressures that shape the brains and cognitive abilities of different species and understanding cognitive processes in differently structured brains. However, our progress on reaching these objectives is slow, mostly because of several major practical challenges. In this review, we discuss 2 major shortcomings: (a) the poor systematics and low magnitude of the phylogenetic comparisons made, and (b) the weak comparability of the results caused by interfering species-specific confounding factors (perceptual, motivational, and morphological) alongside an insufficient level of standardisation of the methodologies. We propose a multiple-level comparative approach that emphasises the importance of achieving more direct comparisons within taxonomic groups at genus or family level as the first step before comparing between distantly related groups. We also encourage increasing interdisciplinary efforts to execute "team-science" approach in building a systematic and direct large-scale phylogenetic comparisons of bigger cognitive test batteries that produce reliable species-representative data. We finally revisit some existing suggestions that allow us to maximise standardisation while minimising species-specific confounding factors. (PsycInfo Database Record (c) 2020 APA, all rights reserved).