The convective flow of liquid metal inside the Earth's outer core sustains the Earth's magnetic field against Ohmic decay. The resulting nonlinear process, termed the geodynamo, operates on a wide range of time and length scales. Direct and indirect observations of the geomagnetic field at the Earth's surface document the variability of the geodynamo over the archeological, historical and modern periods, with increasing accuracy. These observations are slaved to changes in the magnetic field at the core-mantle boundary (CMB), that is the top of the region in which the geodynamo operates. The motivation behind considering the application of data assimilation techniques in geomagnetism is at least twofold: first, to combine data and physics to better constrain the state of Earth's core (at the CMB and below), and second, to forecast the evolution of the geomagnetic field. After a general introduction to the problem at hand, we will report on the application of the ensemble Kalman filter to a numerical dynamo model, whose state vector comprises 106 variables. Our strategy rests on a modified version of the parallel data assimilation framework of Nerger & Hiller (Comp. & Geosci., 2013). Our synthetic tests demonstrate the efficacy and adaptivity of the method, provided the ensemble comprises O(500) members, in which case the typical spin-up time of the system is O(1000) years. We will show that the model we used for these proof-of-concept experiments is not so well-suited for the assimilation of real datasets, and we will conclude this presentation by discussing how it should be improved, and what this improvement implies in terms of computational and storage requirements.