Swarm behaviors are common in nature, where individual organisms collaborate via perception, communication, and adaptation. Emulating these dynamics, large groups of active agents can self-organize through localized interactions, giving rise to complex swarm behaviors, which exhibit potential for applications across various domains. This review presents a comprehensive summary and perspective of synthetic swarms, to bridge the gap between the microscale individual agents and potential applications of synthetic swarms. We begin by examining active agents, the fundamental units of synthetic swarms, to understand the origins of their motility and functionality in the presence of external stimuli. Then we summarize inter-agent communications and agent-environment communications that contribute to the swarm generation. Furthermore, we review the swarm behaviors reported to date and the emergence of machine intelligence within these behaviors. Eventually, the applications enabled by distinct synthetic swarms are summarized. By discussing the emergent machine intelligence in swarm behaviors, we offer insights into the design and deployment of autonomous synthetic swarms for real-world applications. This article is protected by copyright. All rights reserved.