In this paper, we propose a novel Space-Time Shift Keying (STSK) modulation scheme for MIMO communication systems, where the concept of spatial modulation is extended to include both the space and time dimensions, in order to provide a general shift-keying framework. More specifically, in the proposed STSK scheme one out of Q dispersion matrices is activated during each transmitted block, which enables us to strike a flexible diversity and multiplexing tradeoff. This is achieved by optimizing both the space-time block duration as well as the number of the dispersion matrices in addition to the number of transmit and receive antennas. We will demonstrate that the resultant equivalent system model does not impose any inter-channel interference, and hence the employment of single-stream maximum likelihood detection becomes realistic at a low-complexity. Furthermore, we propose a Differential STSK (DSTSK) scheme, assisted by the Cayley unitary transform, which does not require any Channel ...