In this talk, we consider the online identification of time-varying systems represented by subspaces, relying on tools from manifold optimization. Unlike traditional parametric system models, such as state-space or ARX equations, we represent linear systems as subspaces. This non-parametric model is extensively used in recent data-driven control formulations providing robust and scalable performance. However, online adaptation of the system model remains an open challenge according to recent surveys. Our work aims to address this challenge by proposing methods for identification of linear time-varying systems, which are represented by time-varying subspaces in the considered framework. For this, we formulate the identification task as an optimization problem on the Grassmannian manifold, that encompasses subspaces of a given dimension as points. Online adaptation can be achieved by performing gradient descent on a cost function that incorporates a window of the most recent input-output measurements. Assuming bounds on the signal-to-noise ratio and on the subspace’s rate of change, theoretical guarantees for the resulting algorithm were given in our recent study. Namely, the distance between the estimate and the true subspace is guaranteed to converge with an exponential rate. Furthermore, the effect of noise in the data and the unknown time-variation of the system induces a bias in the upper bound on the distance. The applicability of the resulting method is demonstrated on numerical examples, and it is observed to perform favorably compared to conventional parametric identification techniques.