During the last 10 years, the volume of global data has risen more than tenfold. The commercial rise of cloud computing eased the process of storing, processing and managing big data. Recently, the cloud evolved with the emergence of serverless computing platforms that offer an even more abstracted service model. The elasticity of cloud computing creates significant optimization problems, which can be tackled either with a single objective, or as multi-objective opimization problems (MOO). When it comes to data management, the two main MOO problems in a cloud computing environment are query optimization and task scheduling. Some of the techniques used for solving MOO problems in the cloud are the weighted sum model, mathematical-programming based algorithms and genetic algorithms. We propose the presentation of a tutorial that will underline the main MOO problems of a cloud computing environment in regards to data management, and evaluate the use of serverless computing for such problems. The tutorial will offer the audience a better understanding of current MOO challenges and applications in the cloud, while also giving them an overview of different solutions to such problems and the techniques that can be used for solving them. * The supervisors' names are included in alphabetical order, both contributed equally.