The transition from animal to plant proteins is booming, and the development of meat analogues or alternatives quickly progressing. However, the acceptance of meat analogues by consumers is still limited, mainly due to disappointing organoleptic properties of these foods. The objective of this study was to investigate possible relationships among structure, textural characteristics, consumer acceptance, and sensory evaluation of commercially available meat analogues. The microstructure and texture of 13 chicken analogue pieces and 14 analogue burgers were evaluated with confocal laser scanning microscopy (CLSM) and texture profile analysis (TPA). The moisture of the samples was related to cooking losses and release of liquid upon compression after cooking. Meat products were included as references. A sensory panel (n = 71) evaluated both flavour and texture characteristics. For the chicken analogue pieces, samples with more added fibres had a harder and chewier texture but were less cohesive. No other relations between composition and structure/texture could be found. In the sensory evaluation, lower hardness and chewiness were only seen in products with more fat. A lower sensory hardness was found to be related to the presence of small air pockets. For analogue burgers, there was no clear relation between composition and structure/texture. However, instrumentally measured hardness, chewiness, and cohesiveness correlated well with the corresponding sensory attributes, even though they could not be clearly linked to a structural feature. Next to this, fat content showed a clear correlation to perceived fattiness. CLSM images of burgers with high perceived fattiness showed large areas of fat. Therefore, the release of large fat pools from the meat was most likely responsible for the perception of this attribute. However, perceived fattiness was not related to liking, which was the case also for chicken analogue pieces. For both pieces and burgers, even if some of the measured textural attributes could be linked to the sensory profile, the textural attributes in question could not explain the liking scores. Liking was related to other aspects, such as meaty flavour and juiciness, which were not directly linked to compositional or textural features. Juiciness was not directly related to the moisture loss of the products, indicating that this attribute is rather complex and probably involves a combination of characteristics. These results show that to increase the appreciation of meat analogues by consumers, improving simple texture attributes is not sufficient. Controlling sensory attributes with complex cross-modal perception is probably more important.