With Knowledge Graphs (KGs) at the center of numerous applications such as recommender systems and question-answering, the need for generalized pipelines to construct and continuously update such KGs is increasing. While the individual steps that are necessary to create KGs from unstructured sources (e.g., text) and structured data sources (e.g., databases) are mostly well researched for their one-shot execution, their adoption for incremental KG updates and the interplay of the individual steps have hardly been investigated in a systematic manner so far. In this work, we first discuss the main graph models for KGs and introduce the major requirements for future KG construction pipelines. Next, we provide an overview of the necessary steps to build high-quality KGs, including cross-cutting topics such as metadata management, ontology development, and quality assurance. We then evaluate the state of the art of KG construction with respect to the introduced requirements for specific popular KGs, as well as some recent tools and strategies for KG construction. Finally, we identify areas in need of further research and improvement.