The growing use of Recommender Systems (RS) across various industries, including e-commerce, social media, news, travel, and tourism, has prompted researchers to examine these systems for any biases or fairness concerns. Fairness in RS is a multi-faceted concept ensuring fair outcomes for all stakeholders involved in the recommendation process, and its definition can vary based on the context and domain. This paper highlights the importance of evaluating RS from multiple stakeholders' perspectives, specifically focusing on Tourism Recommender Systems (TRS). Stakeholders in TRS are categorized based on their main fairness criteria, and the paper reviews state-of-the-art research on TRS fairness from various viewpoints. It also outlines the challenges, potential solutions, and research gaps in developing fair TRS. The paper concludes that designing fair TRS is a multi-dimensional process that requires consideration not only of the other stakeholders but also of the environmental impact and effects of overtourism and undertourism.