Computational propaganda is an emergent form of political manipulation that occurs over the Internet. The term describes the assemblage of social media platforms, autonomous agents, algorithms, and big data tasked with the manipulation of public opinion. Our research shows that this new mode of interrupting and influencing communication is on the rise around the globe. Advances in computing technology, especially around social automation, machine learning, and artificial intelligence mean that computational propaganda is becoming more sophisticated and harder to track at an alarming rate. This introduction explores the foundations of computational propaganda. It describes the key role that automated manipulation of algorithms plays in recent efforts to control political communication worldwide. We discuss the social data science of political communication and build upon the argument that algorithms and other computational tools now play an important political role in areas like news consumption, issue awareness, and cultural understanding. We unpack the key findings of the nine country case studies that follow—exploring the role of computational propaganda during events from local and national elections in Brazil to the ongoing security crisis between Ukraine and Russia. Our methodology in this work has been purposefully mixed, we make use of quantitative analysis of data from several social media platforms and qualitative work that includes interviews with the people who design and deploy political bots and disinformation campaigns. Finally, we highlight original evidence about how this manipulation and amplification of disinformation is produced, managed, and circulated by political operatives and governments and describe paths for both democratic intervention and future research in this space.