Blue-veined cheese tends to polarize the consumers’ affective responses due to its strong flavor. This study aims to: (i) explore the consumers’ sensory perceptions and liking of Gorgonzola PDO cheese; (ii) identify the sensory drivers of acceptance for Gorgonzola in the function of the cheese style; (iii) characterize them by the volatile organic compounds (VOCs); and (iv) explore the relationships of the VOCs with sensory perception and liking. Six samples of Gorgonzola cheese differing in style (sweet vs. piquant), aging time (70–95 days), and production process (artisanal vs. industrial) were evaluated by 358 subjects (46% males, 18–77 years) using liking and Rate-All-That-Apply (RATA) tests. The cheese VOCs were measured by SPME/GC-MS. Liking was significantly higher for the sweet cheese than for the piquant cheese and for the artisanal cheese than for the industrial samples. Penalty Analysis showed that ‘creamy’, ‘sweet’, ‘nutty’, and ‘salty’ were significant drivers of liking while the ‘soapy’ and ‘ammonia’ flavors turned out to be drivers of disliking. Fifty-three VOCs were identified. Regression models revealed the significant highest associations between the VOCs and ‘ammonia’, ‘pungent’, ‘soapy’, and ‘moldy’ flavors. A good association was also found with the consumers’ liking. The identification of the sensory drivers of (dis) liking and their relationship with the VOCs of Gorgonzola opens up a new understanding of the consumers’ blue-veined cheese preferences.