Whereas in the Euclidean plane a tiling by congruent tiles consists of topological disks, in Euclidean 3-space, it is possible to have tilings not only by 3-balls but also by congruent genus-\(n\) handlebodies and these can be knotted as well as unknotted. In this paper the author examines tilings of Euclidean 3-space by congruent knotted tiles. All tilings obtained are derived from the tiling of Euclidean space by cubes. One first method described is based on decomposing the cube into three pieces of which two are solid balls. These tilings are completely described by the following theorem: If a cube is decomposed into three polyhedral pieces, two of which are balls, and the third of which is contained in the interior of the cube, then the third must be a ball or a cube-with-holes, i.e. a cube with a certain number of possibly knotted and tangled tunnels drilled out of it. In particular this shows that a solid knotted torus cannot be obtained in this simple way. In fact three rather than two balls have to be used to fill up surrounding space. Getting on to more complex tile shapes the author finally shows how to tile with Euclidean 3-space with tiles that are topologically of any polyhedral shape possible. In a final section he shows how to generalize the tilings to spherical and hyperbolic 3-space using tiles based on the dodecahedral tiling of these spaces, and to tilings of Euclidean \(n\)-space, using tiles based on the tiling by hypercubes. The paper ends with a few open questions.