Research on graphene and other two-dimensional atomic crystals is intense and likely to remain one of the hottest topics in condensed matter physics and materials science for many years. Looking beyond this field, isolated atomic planes can also be reassembled into designer heterostructures made layer by layer in a precisely chosen sequence. The first - already remarkably complex - such heterostructures (referred to as 'van der Waals') have recently been fabricated and investigated revealing unusual properties and new phenomena. Here we review this emerging research area and attempt to identify future directions. With steady improvement in fabrication techniques, van der Waals heterostructures promise a new gold rush, rather than a graphene aftershock.