Cosmic strings are linear topological defects which are expected to form during symmetry-breaking phase transitions in the early universe. In addition, some inflation models based on string theory predict that fundamental strings and D-strings could grow to cosmic scales and constitute a network of cosmic superstrings. When forming loops, cosmic strings radiate energy through bursts of gravitational waves in the presence of cuspy features. This mechanism represents one of the most promising observational signatures to detect the existence of cosmic strings. The sensitivity of ground-based gravitational-wave detectors LIGO and Virgo allows us to explore an unconstrained region of the cosmic string parameter space. After reviewing the cosmic string models and the targeted gravitational-wave signals, we present the search for cosmic string burst signals which has been conducted over 5 years of joint LIGO-Virgo data. We discuss the astrophysical impact of this search and the future prospects for the advanced detectors era.