Increasing consumer demand for high-quality, additive-free fruit and vegetable products with ‘fresh-like’ sensory properties has led to the development of novel ‘minimal processing’ technologies. As a prime example, high pressure processing (HPP) is increasingly applied as an alternative to thermal processing (TP) to maintain the properties of fresh fruit-based juices and smoothies. However, the resulting products need to be validated from a sensory standpoint. Situated within this context, this paper provides a narrative review of sensory studies focused on high pressure treated fruit juices and smoothies published in the last ≈25 years (1995 to 2021), centered around three objectives: (i) to review methods used for assessing the sensory quality, (ii) to review knowledge of the effect of HPP on sensory quality, and (iii) to understand consumers’ acceptability towards these products. Overall, most sensory studies concluded that a combination of HPP and low temperature storage preserved the sensory properties better than TP, and thereby enables the production of products with ‘fresh-like’ quality. Yet, most published studies employed very small panel sizes and often showed a mismatch between test type and assessors employed (for example, using consumers for analytic tests and trained assessors for affective tests), which might lead to biased results. In future research, a clearer focus on experimental conditions, proper sensory methods, and more focus on the relationship between sensory quality and consumer perception are needed to better understand the effect of HPP on the sensory quality of fruit juices and smoothies.