It is not unusual to experience a sense of total absorption, concentration, action-awareness, distortion of time and intrinsic enjoyment during an activity that involves music. Indeed, it is noted that there is a special relationship between these two aspects (i.e., music and flow experience). In order to deeply explore flow in the musical domain, it is crucial to consider the complexity of the flow experience—both as a “state” and as a “trait.” Secondly, since music is a multifaceted domain, it is necessary to concentrate on specific music settings, such as (i) musical composition; (ii) listening; and (iii) musical performance. To address these issues, the current review aims to outline flow experience as a “trait” and as a “state” in the three above-mentioned musical domains. Clear and useful guidelines to distinguish between flow as a “state” and as a “trait” are provided by literature concerning flow assessment. For this purpose, three aspects of the selected studies are discussed and analyzed: (i) the characteristics of the flow assessments used; (ii) the experimental design; (iii) the results; and (iv) the interrelations between the three domains. Results showed that the dispositional approach is predominant in the above-mentioned settings, mainly regarding music performance. Several aspects concerning musical contexts still need to be deeply analyzed. Future challenges could include the role of a group level of analysis, overcoming a frequency approach toward dispositional flow, and integrating both state and dispositional flow perspectives in order to deepen comprehension of how flow takes place in musical contexts. Finally, to explain the complex relationship between these two phenomena, we suggest that music and flow could be seen as an emergent embodied system.