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The study of kink interactions in nonlinear Klein-Gordon models in$1+1$-dimensions has a time-honored history. Until a few years ago, it wasarguably considered a fairly mature field whose main phenomenology was wellunderstood both qualitatively and at least semi-quantitatively. This consensuswas shattered when H. Weigel and his group established that the effective modelthat had allowed this detailed understanding contained an all-important typo.Remarkably, they found that correcting this error wipes out both thequantitative and qualitative agreement and, in fact, leads to additionalproblems.  We summarize the history of the subject from the early studies, up toWeigel's work and reflect on where these recent developments leave ourunderstanding (which, quantitatively, is close to square one!).  Importantly, we stress a number of emerging additional directions that havearisen in higher-order power law models and speculate on the associatedsignificant potential for future work.

Four Decades of Kink Interactions in Nonlinear Klein-Gordon Models: A Crucial Typo, Recent Developments and the Challenges Ahead