Context. The halo of the Milky Way has long been hypothesized to harbour significant amounts of merger debris. For more than a decade this view has been supported by wide-field photometric surveys which have revealed the outer halo to be lumpy. Aims. The recent release of Gaia DR2 is allowing us to establish that mergers also have been important and possibly built up the majority of the inner halo. In this work we focus on the Helmi streams, a group of streams crossing the solar vicinity and known for almost two decades. We characterize their properties and relevance for the build-up of the Milky Way's halo. Methods. We identify new members of the Helmi streams in an unprecedented dataset with full phase-space information combining Gaia DR2...