Objects with rhythms naturally synchronize. Synchronizationis the coordination of events in order to run the systemuniformly. Yet the phenomenon went entirely undocumenteduntil 1665. Since the pioneering description of synchronizationby Huygens, the phenomenon has been studied by variousresearchers in an interdisciplinary manner. Many researchershave contributed to the development of synchronizationtheory proving that synchronization occurs in couplednon-linear dissipative oscillators. Such oscillators rangefrom mechanical clocks and population dynamics to humanheart and neural networks. This article aims to explain thebasic principles of synchronization theory. The history andapplications of synchronization are discussed in real-worldscenarios. We address different types of synchronization witha detailed discussion on the simplest type of synchronization.The phenomenon of synchronization applies to oscillations ofdifferent forms—periodic, noisy, and chaotic in nature. Here,we specifically discuss the oscillators which can hold synchronization.In particular, we provide an overview of self-sustainedperiodic and chaotic oscillators with a detailed description ofdifferent forms of these oscillators in phase space. Further, asummary of further research challenges has also been givenfor the future development of advanced applications based onnatural synchronization phenomenon.