In this talk we discuss sharp weighted Finsler-Hardy inequalities and trace Finsler-Hardy inequalities. We follow a unifying approach, by starting with a sharp interpolation between them, in the half-space, extending the corresponding non-weighted version, being established recently by a different approach. Then, passing to bounded domains, we obtain successive sharp improvements by adding Hardy-type remainder terms, resulting in an infinite series-type improvement. The optimality of the weights and the constants of the remainder terms, and the application of our method in cones, are also discussed. These results extends, into the Finsler context, the earlier known ones within the Euclidean setting.