The premise for How I Met Your Mother is that Future Ted is telling his two children the story of how he met their mother, revealing more of the story in each episode. The son and daughter appear to be in their early to mid-teens in the year 2030, which is when Ted sits the kids down to tell them the story.

Their names remained unknown throughout most of the series, however it has been shown Ted wanted to name them Luke and Leia, after the two Star Wars characters.

Ted finally finishes telling the kids the story of how he met their mother. Penny figures out that the reason Ted told them that story was so they could understand how much Ted also loved their Aunt Robin. Both Penny and Luke then go on and encourage Ted to pursue Robin.