We give an extension of Scholze's theory of shtukas to non-reductive groups. We compute a simple example of such a moduli of shtukas, and show that in this case, the period morphism is related to the logarithm. We also give an exposition of the objects appearing in this theory, and mention two joint results of the author: the open mapping theorem for complete analytic Huber rings, and a characterization of extensions of semistable vector bundles on the Fargues-Fontaine curve.