In the past few years, there has been a growing demand by consumers for more complex beers with distinctive organoleptic profiles. The yeast, raw material (barley or other cereals), hops, and water used add to the major processing stages involved in the brewing process, including malting, mashing, boiling, fermentation, and aging, to significantly determine the sensory profile of the final product. Recent literature on this subject has paid special attention to the impact attributable to the processing conditions and to the fermentation yeast strains used on the aromatic compounds that are found in consumer-ready beers. However, no review papers are available on the specific influence of each of the factors that may affect beer organoleptic characteristics. This review, therefore, focuses on the effect that raw material, as well as the rest of the processes other than alcoholic fermentation, have on the organoleptic profile of beers. Such effect may alter beer aromatic compounds, foaming head, taste, or mouthfeel, among other things. Moreover, the presence of spoilage microorganisms that might lead to consumers’ rejection because of their impact on the beers’ sensory properties has also been investigated.