Bridges are designed and built to be safe against failure and perform satisfactorily over their service life. Bridge structural health monitoring (BSHM) systems are therefore essential to ensure the safety and serviceability of such critical transportation infrastructure. Identification of structural damage at the earliest time possible is a major goal of BSHM processes. Among many developed damage identification techniques (DITs), vibration-based techniques have shown great potential to be implemented in BSHM systems. In a vibration-based DIT, the response of a bridge is measured and analyzed in either time or space domain for the purpose of detecting damage-induced changes in the extracted dynamic properties of the bridge. This approach usually requires a comparison between two structural states of the bridge—the current state and a reference (intact/undamaged) state. In most in-situ cases, however, data on the bridge structural response in the reference state are not available. Therefore, researchers have been recently working on the development of DITs that eliminate the need for a prior knowledge of the reference state. This paper thoroughly explains why and how the reference state can be excluded from the damage identification process. It then reviews the state-of-the-art reference-free vibration-based DITs and summarizes their merits and shortcomings to give guidance on their applicability to BSHM systems. Finally, some recommendations are given for further research.