The Severi problem concerns the irreducibility of the scheme \(V^{\mathrm{irr}}_{g,d}\) that parametrizes irreducible projective plane curves of fixed degree \(d\) and geometric genus \(g\). In characteristic \(0\), the irreducibility was finally proved by J. Harris [Invent. Math. 84, 445–461 (1986; Zbl 0596.14017)], based on a result by M. Artin (ed.) and J. Tate (ed.) [Arithmetic and geometry. Papers dedicated to I. R. Shafarevich on the occasion of his sixtieth birthday. Vol. II: Geometry. Boston-Basel-Stuttgart: Birkhäuser (1983; Zbl 0518.00005)] that bounds the dimension of the irreducible components of \(V^{\mathrm{irr}}_{g,d}\) and describes curves parametrized by general points in the components. Zariski’s and Harris’ proofs require degeneration arguments that do not apply immediately in positive characteristic. In the paper under review, the authors apply a degeneration to tropical objects to extend the solution of the Severi problem to plane curves defined over an algebraically closed field of any characteristic. Indeed, by means of a tropical degeneration, the authors prove that the closure of any component \(V\) of the variety \(V_{g,d}\) that parametrizes (possible reducible) curves of degree \(d\) and genus \(g\) contains the variety \(V_{1-d,d}\). As a consequence, the authors obtain that \(V\) has dimension \(\leq 3d+g-1\) and its general point parametrizes a nodal curve. Directly from the degeneration argument, the authors then prove the irreducibility of \(V^{\mathrm{irr}}_{g,d}\), for all \(g\geq 0\).