Enterprises are moving their business critical workloads to public clouds at an accelerating pace. Cloud data services for Online Transaction Processing (OLTP), Data Analytics and NoSQL are essential building blocks for enterprise applications. Multi-tenancy is a crucial tenet for cloud data service providers that allows sharing of data center resources across tenants, thereby reducing cost. In this monograph, the authors review architectures of today's cloud data services and identify trends and challenges that arise in multi-tenant cloud data services. They survey techniques that have been developed for enabling elasticity, providing SLAs, ensuring performance isolation and reducing cost. The emerging paradigm of serverless databases is reviewed and opportunities and challenges highlighted. Finally, the authors identify open research problems in the fast-changing landscape of cloud data services. This timely overview, written by recognized experts in the field provides readers with essential insights into designing cloud data services to day and in the future. This concise and accessible review will save designers and researchers hours by having it at their fingertips.