Revealed more than two millennia ago by Pythagoras, consonance and dissonance (C/D) are foundational concepts in music theory, perception, and aesthetics. The search for the biological, acoustical, and cultural factors that affect C/D perception has resulted in descriptive accounts inspired by arithmetic, musicological, psychoacoustical or neurobiological frameworks without reaching a consensus. Here, we review the key historical sources and modern multidisciplinary findings on C/D and integrate them into three main hypotheses: the vocal similarity hypothesis (VSH), the psychocultural hypothesis (PH), and the sensorimotor hypothesis (SH). By illustrating the hypotheses-related findings, we highlight their major conceptual, methodological, and terminological shortcomings. Trying to provide a unitary framework for C/D understanding, we put together multidisciplinary research on human and animal vocalizations, which converges to suggest that auditory roughness is associated with distress/danger and, therefore, elicits defensive behavioral reactions and neural responses that indicate aversion. We therefore stress the primacy of vocality and roughness as key factors in the explanation of C/D phenomenon, and we explore the (neuro)biological underpinnings of the attraction-aversion mechanisms that are triggered by C/D stimuli. Based on the reviewed evidence, while the aversive nature of dissonance appears as solidly rooted in the multidisciplinary findings, the attractive nature of consonance remains a somewhat speculative claim that needs further investigation. Finally, we outline future directions for empirical research in C/D, especially regarding cross-modal and cross-cultural approaches.