Over a hundred gravitational-wave signals have now been detected from the mergers of black holes and neutron stars, but other sources of gravitational waves have not yet been discovered. Some of the most violent explosive events in the Universe are predicted to emit bursts of gravitational waves, and may result in the next big multi-messenger discovery. Potential new sources of gravitational-wave bursts include core-collapse supernovae, cosmic strings, fast radio bursts, magnetars, eccentric compact binary systems and pulsar glitches. Gravitational-wave burst signals often have an unknown waveform shape, and unknown gravitational-wave energy, due to unknown or very complicated progenitor astrophysics. In this talk, I will describe the detection prospects for gravitational-wave bursts from new sources, and discuss the challenges of searching for gravitational-wave burst signals and interpreting the astrophysics of the source.