Research on temporal knowledge bases, which associate a relational fact (s, r, o) with a validity time period (or time instant), is in its early days.Our work considers predicting missing entities (link prediction) and missing time intervals (time prediction) as joint Temporal Knowledge Base Completion (TKBC) tasks, and presents TIMEPLEX, a novel TKBC method, in which entities, relations and, time are all embedded in a uniform, compatible space.TIMEPLEX exploits the recurrent nature of some facts/events and temporal interactions between pairs of relations, yielding stateof-the-art results on both prediction tasks.We also find that existing TKBC models heavily overestimate link prediction performance due to imperfect evaluation mechanisms.In response, we propose improved TKBC evaluation protocols for both link and time prediction tasks, dealing with subtle issues that arise from the partial overlap of time intervals in gold instances and system predictions.