Ever since Ernest Rutherford scattered alpha-particles from gold foils(1), collision experiments have revealed insights into atoms, nuclei and elementary particles(2). In solids, many-body correlations lead to characteristic resonances(3)-called quasiparticles-such as excitons, dropletons(4), polarons and Cooper pairs. The structure and dynamics of quasiparticles are important because they define macroscopic phenomena such as Mott insulating states, spontaneous spin-and charge-order, and high-temperature superconductivity(5). However, the extremely short lifetimes of these entities(6) make practical implementations of a suitable collider challenging. Here we exploit lightwave-driven charge transport(7-24), the foundation of attosecond science(9-13), to explore ultrafast quasiparticle collisions directly in the time domain: a femtosecond optical pulse creates excitonic electron-hole pairs in the layered dichalcogenide tungsten diselenide while a strong terahertz field accelerates and collides the electrons with the holes. The underlying dynamics of the wave packets, including collision, pair annihilation, quantum interference and dephasing, are detected as light emission in high-order spectral sidebands(17-19) of the optical excitation. A full quantum theory explains our observations microscopically. This approach enables collision experiments with various complex quasiparticles and suggests a promising new way of generating sub-femtosecond pulses.