Knots and links have been conjectured to play a fundamental role in a wide range of physical fields, including plasmas and fluids, both quantum and classical. In fluids, the fundamental knottedness-carrying excitations occur in the form of linked and knotted vortex loops, which have been conjectured to exist for over a century. Although they have been the subject of considerable theoretical study, their creation in the laboratory has remained an outstanding experimental goal. Here we report the creation of isolated trefoil vortex knots and pairs of linked vortex rings in water using a new method of accelerating specially shaped hydrofoils. Using a high-speed scanning tomography apparatus, we measure their three-dimensional topological and geometrical evolution in detail. In both cases we observe that the linked vortices stretch themselves and then deform—as dictated by their geometrically determined energy—towards a series of local vortex reconnections. This work establishes the existence and dynamics of knotted vortices in real fluids.