A rapidly growing demand on transmission rates, coverage and reliability for wireless communication systems has triggered an intensive research in the field of multi-antenna communications. The use of multi-antenna systems provides significant gains by making use of independent propagation paths between the transmitter and the receiver. Space-time coding has been recently proposed to exploit the benefits of the multi-antenna channels. In space-time code design, different tradeoffs have to be taken into account. Good codes should provide a high diversity gain and achieve the highest possible multiplexing gain. At the same time, the encoding/decoding complexity should remain as low as possible to enable computationally efficient signal processing. In this thesis, we propose high-rate high-performance space-time block coding schemes that achieve a significantly reduced maximum likelihood decoding complexity in comparison to other state-of-the-art space-time codes. In particular, we propose a 2x2 full-rate space-time code with non-vanishing determinants that achieves the optimal diversity-multiplexing gain tradeoff while using a fast maximum likelihood decoder. Furthermore, by extending the proposed strategy, we develop space-time codes for 3 and 4 transmit antennas. In certain cases, the use of multi-antenna systems can become impractical due to restrictions in hardware size and cost. As an alternative to create multi-path propagation environments, half-duplex wireless relay networks have emerged. In such networks, single antenna users cooperate to provide gains similar to that of the multi-antenna channel. Considering the initial restrictions, low-complexity distributed space-time coding schemes are required for relay systems. In the second part of the thesis, we develop a novel low-rate feedback-based distributed approach for cooperative transmission in relay networks that achieves the maximum diversity offered by the relay network, enjoys low-complexity maximum likelihood decoding, avoids long decoding delays and is applicable to any number of relays. The use of second-order channel statistics to design “long-term” power control weights is considered to further improve the performance of our approach in practical scenarios with channel links of different quality. Moreover, the proposed distributed space-time coding schemes are generalized to the non-coherent receiver case using differential transmission.