The field of Neural Style Transfer (NST) has witnessed remarkable progress in the past few years, with approaches being able to synthesize artistic and photorealistic images and videos of exceptional quality. To evaluate such results, a diverse landscape of evaluation methods and metrics is used, including authors' opinions based on side-by-side comparisons, human evaluation studies that quantify the subjective judgements of participants, and a multitude of quantitative computational metrics which objectively assess the different aspects of an algorithm's performance. However, there is no consensus regarding the most suitable and effective evaluation procedure that can guarantee the reliability of the results. In this review, we provide an in-depth analysis of existing evaluation techniques, identify the inconsistencies and limitations of current evaluation methods, and give recommendations for standardized evaluation practices. We believe that the development of a robust evaluation framework will not only enable more meaningful and fairer comparisons among NST methods but will also enhance the comprehension and interpretation of research findings in the field.