Abstract. Finite geometry has long established connections with coding theory, both classically in the Hamming metric, and more recently for the rank and sum-rank metrics. In particular, constructions and classifications of arcs, scattered subspaces, and evasive subspaces lead to corresponding results for codes. In the rank metric, algebraic approaches using linearised polynomials, skew polynomial rings, and finite semifields have proven very powerful for constructions. In this talk we will give an overview of some of these methods in the rank metric, and report on recent work (joint with Paolo Santonastaso) on some recent surprising applications of these methods in the sum-rank metric.