In this talk, we will introduce a new numerical method for the approximation of nonlinear, transient stress-diffusion problems and apply them to the solution of strongly coupled problems of hydrogen transport in deformable media. More precisely, we will address the approximate solution of elastic and inelastic mechanical problems of metals exposed to transient concentrations of hydrogen. We will be interested in the modification of the mechanical properties of the host due to the hydrogen content and the changes in the diffusion phenomenon due to the stress field. The numerical methods we will describe are based on the concept of variational updates. In this family of methods, all the unknown fields (both mechanical and chemical) are obtained from the stationary conditions of a single (incremental) functional. Such methods have several advantages over conventional ones; in particular, in the case of implicit solutions, the tangent operators are always symmetric, leading to significant computational savings. In the talk, based on our recent work [1], we will present the theory for this new class of methods and show examples that involve the elastic and the elastoplastic behavior of steels subject to hydrogen atmosphere.