The process of micro-milling is a promising technology for the fabrication of micro-parts with arbitrary 3D features in a wide range of materials. However, as a result of the reduced dimensions, the susceptibility of the process for machine tool errors and vibrations is higher, having adverse effects on accuracy and surface quality of the resulting workpieces. Furthermore, the production time and the efficiency of the process suffer from low material removal rates and excessive tool wear and breakage. To improve the micro-milling process, online process monitoring and control becomes of high importance. Signs of problems are almost unnoticeable without the use of special equipment. Techniques are needed to detect and possibly even predict anomalies in the process and to online monitor the condition of the cutting process. Spindles with Active Magnetic Bearings are particularly interesting for the micro-milling process, not only for the achievable spindle speeds, but also because of the opportunities they offer to develop online process monitoring and control techniques. These include force monitoring, tool condition and breakage monitoring, and chatter control. However, literature thus far lacks results implementing these techniques for the micro-milling process. The aim of this thesis is to investigate the opportunities for model-based process monitoring and control to improve the micro-milling process using the intrinsic properties of AMB spindles. This objective is narrowed down to the goal of estimating the cutting forces from the bearing signals. The approach towards this goal consists of three steps. First an approach to model-based cutting force estimation in micro-milling using the signals of the AMBs is developed. The cutting force estimation problem is expressed as an input estimation problem, where the cutting forces are an unknown input to the closed-loop AMB spindle system. To solve this problem, a method is given for model-based optimal estimation of unknown inputs to multivariable closed-loop systems, based on Wiener filter theory. For cases in which controller knowledge is not available, an approach is formulated in which equal performance of the estimator is ensured for any controller. Smoothed estimators are derived, resulting in smaller estimation errors when a delay in the estimation result is tolerable. Second, a method is presented for system identification of a high speed AMB micro-milling spindle in the frequency range relevant for force estimation. This problem is separated into two subproblems. The first is the identification of the dynamics from the current input to the displacement of the rotor shaft at the bearings, the bearing dynamics. The second problem is the identification of the tooltip dynamics, which are the dynamics between the force on the tooltip and the displacement of the rotor shaft at the bearings. System identification of the bearing dynamics is approached by first making a non-parametric estimate of the multivariable frequency response function (FRF). An experiment design is given targeted at yielding small bias and variance of the FRF, as well as small error due to nonlinear distortions. Using the FRF estimate, a multivariable parametric model is estimated. Here, the main emphasis is on identification of a parametric model of the plant dynamics, leading to the choice of minimization of an output error (OE) criterion. An IV-based algorithm is given for estimation of multi-input multi-outout (MIMO) Output Error models in matrix fraction description from frequency domain data. This algorithm has the property that convergence of the iterations implies that an optimal solutions has been found. The main challenge in identifying the tooltip dynamics is to apply a known excitation force to the tooltip. The route followed in this thesis is to identify the tooltip dynamics using data obtained during a milling experiment in which the cutting forces are measured. The amount of data that can be generated in this way is limited, as is the control over the spectral properties of the input. Hence, in order to reduce the complexity of the identification, usage is made of assumed observability and controllability properties of the system. This results in a particular closed-loop parameterization of the model-set and a known, but non-minimum phase noise model. For this particular identification problem, solutions are formulated. The third and last step to the goal of this thesis pertains to model-based correction of runout disturbances in measurements of the positions and currents of AMB spindle. Such disturbances are synchronous with the rotation of the spindle and hence almost periodic. A parametrized truncated Fourier series expansion model for the runout disturbance as a function of the angular position is used, allowing to formulate runout identification as a parameter estimation problem. In correcting for the runout disturbances, the main issue is how to deal with the uncertainty in the angular position measurements, or the total lack of such measurements. Solutions are given that compensate for the errors introduced by this uncertainty, or estimate the angular position from the available data using an Extended Kalman filter approach.