Artificial intelligence-empowred Real-Time Bidding (AIRTB) is regarded as one of the most enabling technologies for online advertising. It has attracted significant research attention from diverse fields such as pattern recognition, game theory and mechanism design. Despite of its remarkable development and deployment, the AIRTB system can sometimes harm the interest of its participants (e.g., depleting the advertisers' budget with various kinds of fraud). As such, building trustworthy AIRTB auctioning systems has emerged as an important direction of research in this field in recent years. Due to the highly interdisciplinary nature of this field and a lack of a comprehensive survey, it is a challenge for researchers to enter this field and contribute towards building trustworthy AIRTB technologies. This paper bridges this important gap in trustworthy AIRTB literature. We start by analysing the key concerns of various AIRTB stakeholders and identify three main dimensions of trust building in AIRTB, namely security, robustness and fairness. For each of these dimensions, we propose a unique taxonomy of the state of the art, trace the root causes of possible breakdown of trust, and discuss the necessity of the given dimension. This is followed by a comprehensive review of existing strategies for fulfilling the requirements of each trust dimension. In addition, we discuss the promising future directions of research essential towards building trustworthy AIRTB systems to benefit the field of online advertising.