ELI5 Bed Bugs - why they came back after nearly being eradicated?

What are bed bugs? Can you see them? How long have they been around? We thought we had eradicated them at one point in the mid-20th century but why did they come back? Are there any health risks? How do I tell if I have them, and how does one get rid of bed bugs?
... we explain like I'm five
Thank you to the r/explainlikeimfive community and in particular the following users whose questions and comments formed the basis of this discussion: jigmest, loimographia, animaanon and btrpiii
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