Classification is a fundamental problem in statistical machine learning. It seeks to classify instances into several classes. Binary and multiclass classification settings are the most basic and well-studied settings. Yet, real-world classification problems often involve additional complexities. In this thesis, we focus on complex classification problems in statistical machine learning by exploring three dimensions of complexity: 1) Complex label space; 2) Complex learning setting; 3) Complex performance measure. These complexities pose significant challenges in real-world applications and necessitate the development of novel methodologies that can effectively handle such issues. The goal of my thesis research is to study these complex classification problems.