While Artificial Intelligence (AI) offers many potential benefits in a magnitude of application areas, organizations are still struggling to integrate AI capabilities on a large scale across different business functions. To address this issue, cloud providers offer cloud-based Artificial Intelligence services also known as Artificial-Intelligence-as-a-service (AIaaS). These services aim to support customers in using, developing, deploying, and managing AI capabilities in an easy and flexible way on demand in the cloud. Since AIaaS is a combination of cloud computing and AI, it shares key characteristics of these technologies. Additionally, the combination also yields new AIaaS-specific characteristics leading to increased complexity in service design. There is no one-size-fits-all AIaaS design and consequently, providers face challenges and trade-offs between characteristics that impact the service design and value proposition of AIaaS. To foster an understanding of interdependencies between AIaaS characteristics, trade-offs as well as to assess the consequences of design decisions, this thesis provides an overview of AIaaS-specific characteristics and prevailing trade-offs from a provider’s perspective. Moreover, additional challenges perceived by AIaaS providers are discussed. The results were derived from six conducted semi-structured expert interviews with AIaaS providers. Findings incorporate 10 identified categories of characteristics, each including multiple aspects and a total of 8 identified trade-offs that underline the complexity of AIaaS service design. Furthermore, findings highlight the multitude of design dimensions in AIaaS and suggest that complexity abstraction and performance characteristics are central to most of the identified trade-offs.