Alternatives to the conventional thermal processing (TT) of food are an area of research that has grown tremendously in recent decades. The impact of these alternative techniques on the sensory profile of fruit juices has been discussed in the literature but only in a fragmented manner. This review takes a macroscopic approach to discuss the influence of emerging thermal and non-thermal techniques currently used by industries on a commercial scale, like high-pressure processing (HPP), ohmic heating (OH), and pulse electric field processing (PEF), on certain sensory characteristics of fruit juices and beverages. A sensory impression of a product is a result of a complex mixture of several compounds. The sensory profile varies with the type of processing technique due to differences in intensities and the inactivation mechanism for enzymes. Heat plays a role in the generation of flavor and odor-active compounds; hence, a different sensory profile is expected with alternative techniques that operate at ambient temperatures (HPP and PEF) or have short treatment time due to rapid heating (OH). HPP, OH, and PEF positively influence the retention of compounds that contribute to a fresh-like sensory experience. However, enzyme inactivation is often challenging with alternative techniques resulting in higher residual activity, affecting sensory quality during storage. Nevertheless, there is evidence in the literature of products with stable sensory properties during storage after processing with alternative techniques. Additionally, some residual enzyme activity may play a role in flavor enhancement during storage, i.e., the release of aglycones from glycoconjugates by pectolytic enzymes. Multiple factors like fruits’ cultivar, way of cultivation, external growth conditions, and maturity stage at the time of harvest influence its sensory quality and, subsequently, the products derived from them. The review concludes with the impression that there is extensive literature on the effects of HPP on the sensory properties of fruit juices. However, the research is limited in discussing the influence of OH and PEF. Additionally, it is difficult to make a fair and systematic comparison among the different preservation technologies because of the lack of standardization and comprehensive sensory evaluation in the studies in the literature.