Cooperative communications is a promising technique for future high speed wireless communications. These systems may be formulated as virtual multi-input multi-output (MIMO) systems where spatial/cooperetive diversity is a key advantage. However, different from MIMO systems, one of the major challenges for cooperative communications systems is that the cooperative transmissions in cooperative systems may be neither time nor frequency synchronized, since the transmissions are from multiple cooperative nodes at different locations. The existing signal designs for co-located MIMO systems may not be able to collect the cooperative diversity in cooperative communications systems. This paper gives an overview of recent research efforts on combating the time and frequency asynchronism of the cooperative communication network. We focus on the signal designs (or space-time codings/modulations) to achieve full cooperative diversity, and summarize some of the resent distributed space-timing coding and space-frequency coding techniques to combat timing errors and frequency offsets, and in the meantime to achieve full cooperative diversity, in both one-way and two-way cooperative networks.