Machine learning engineering (MLE) agents are emerging as a new paradigm for automating end-to-end ML pipeline development. Using large language models for code generation and predictive performance as a machine-gradable feedback signal, these agents iteratively synthesize, execute, and refine pipeline code. Yet current systems are largely evaluated on pre-built, single-table benchmarks that abstract away key data management challenges. This tutorial introduces the foundations of MLE agents and highlights research opportunities for the database community. We cover how agents combine program synthesis with iterative and evolutionary optimization, and discuss open challenges in efficient pipeline execution, data discovery and augmentation over heterogeneous sources, reliability and debugging, as well as fairness and compliance. We connect these challenges to existing data management techniques and conclude with a hands-on session using contemporary MLE agents.