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Two new transmit/receive (Tx/Rx) antenna selection strategies are proposed and analyzed for two-way multiple-input multiple-output (MIMO) amplify-and-forward (AF) relay networks. These two strategies select the best transmit and receive antennas at the two sources and the relay based on (i) minimizing the overall outage probability and (ii) maximizing the sum-rate. The performance of these selection strategies is quantified by deriving the overall outage probability, its high SNR approximation and the diversity order providing valuable insights into practical system-designs. Importantly, multiple relay and multiple user two-way relay network set-ups are also treated by proposing and analyzing (i) joint relay and antenna selection strategies, and (ii) joint user, relay and antenna selection strategies, respectively. Interestingly, our outage probability results reveal that the joint relay and antenna selection strategies achieve significant diversity and array gains over those of their single relay counterparts. In fact, the diversity orders of individual relayed-branches accumulate to yield the overall diversity of the multi-relay networks. For example, at 10-2 outage probability, the dual-antenna relay provides a 14 dB gain over a single-antenna relay, and having two dual-antenna relays improves the gain by another 5 dB. Moreover, the performance degradation due to practical transmission impairments (i) feedback delays, (ii) spatially-correlated fading and (iii) non-identically distributed fading is quantified. Impact of channel prediction to circumvent outdated channel state information for antenna selection due to feedback delay is also studied. All the derivations are validated through Monte-Carlo simulations.