Stablecoins, with a capitalization exceeding 200 billion USD as of January 2025, have shown significant growth, with annual transaction volumes exceeding 10 trillion dollars in 2023 and nearly doubling that figure in 2024. This exceptional success has attracted the attention of traditional financial institutions, with an increasing number of governments exploring the potential of Central Bank Digital Currencies (CBDCs). Although academia has recognized the importance of stablecoins, research in this area remains fragmented, incomplete, and sometimes contradictory. In this paper, we aim to address the cited gap with a structured literature analysis, correlating recent contributions to present a picture of the complex economic, technical, and regulatory aspects of stablecoins. To achieve this, we formulate the main research questions and categorize scientific contributions accordingly, identifying main results, data sources, methodologies, and open research questions. The research questions we address in this survey paper cover several topics, such as the stability of various stablecoins, novel designs and implementations, and relevant regulatory challenges. The studies employ a wide range of methodologies and data sources, which we critically analyze and synthesize. Our analysis also reveals significant research gaps, including limited studies on security and privacy, underexplored stablecoins, unexamined failure cases, unstudied governance mechanisms, and the treatment of stablecoins under financial accounting standards, among other areas.