Unlike concrete words related to sensory perception (e.g., hear, sun), abstract words (including the words with temporal semantics, e.g., year, tomorrow) do not have direct embodied sensory correlates. Nevertheless, existing research indicates that abstract concepts’ representations make regular reference to sensorimotor processes, e.g., visual perception. For example, regular expressions such as “the future is ahead” or “the flow of time” are common in different languages reflecting a relatively universal nature of space-time correspondences. Moreover, these regular correspondences are commonly demonstrated in experimental studies; for example — by registering attentional displacement during processing of past and future related words. Here, the main theoretical approaches as well as existing experimental data documenting neurocognitive foundations of space-time representations are reviewed. A detailed overview of research on spatial-conceptual mapping of time concepts in three-dimensional visual space is offered. We also consider features of space-time associations that reflect linguistic and socio-cultural differences. In conclusion, the main areas of current and future that will allow an integration of the existing data within a common theoretical framework are defined.