The proliferation of sixth-generation (6G) networks and the massive Internet of Things (IoT) demand wireless communication technologies that are ultra-low-power, secure, and covert. Noise-based communication has emerged as a transformative paradigm that meets these demands by encoding information directly into the statistical properties of noise, rather than using traditional deterministic carriers. This survey provides a comprehensive synthesis of this field, systematically exploring its fundamental principles and key methodologies, including thermal noise modulation (TherMod), noise modulation (NoiseMod) and its variants, and the Kirchhoff-law-Johnson-noise (KLJN) secure key exchange. We address critical practical challenges such as channel estimation and hardware implementation, and highlight emerging applications in simultaneous wireless information and power transfer (SWIPT) and non-orthogonal multiple access (NOMA). Our analysis confirms that noise-based systems offer unparalleled advantages in energy efficiency and covertness, and we conclude by outlining future research directions to realize their potential for enabling the next generation of autonomous and secure wireless networks.