This talk deals with the problem of identifying and estimating dynamical parameters of continuous-time quantum open systems, in the input-output formalism. I will discuss several aspects of this problem: The first aspect concerns the structure of the space of identifiable parameters for ergodic dynamics, assuming full access to the output state for arbitrarily long times. I will show that the equivalence classes of undistinguishable parameters are orbits of a Lie group acting on the space of dynamical parameters. The second aspect concerns the information geometric structure on this space. I will show that the space of identifiable parameters is the base space of a principal bundle given by the action of the group, and carries a Riemannian metric based on the quantum Fisher information of the output. The metric can be computed explicitly in terms of the Markov covariance of certain "fluctuation operators", and relate it to the horizontal bundle of the connection. The third aspect concerns the asymptotic statistical structure of the output state. I will show that the output state satisfy local asymptotic normality, i.e. they can be approximated by a Gaussian model consisting of coherent states of a multimode continuos variables system constructed from the Markov covariance ``data". The forth direction explores the properties of systems which are near a “dynamical phase transition”. I will show that this is ofter accompanied by a Heisenberg scaling of the quantum Fisher information for long times of the order of the correlation time. Related to this is the phenomenon of metastability which will be briefly discussed. References: [1] Madalin Guta, Jukka Kiukas Information geometry and local asymptotic normality for multi-parameter estimation of quantum Markov dynamics arXiv:1601.04355 [2] Katarzyna Macieszczak, Madalin Guta, Igor Lesanovsky, Juan P. Garrahan Dynamical phase transitions as a resource for quantum enhanced metrology arXiv:1411.3914 (to appear in Phys,. Rev. A) [3] Katarzyna Macieszczak, Madalin Guta, Igor Lesanovsky, Juan P. Garrahan Towards a theory of metastability in open quantum dynamics arXiv:1512.05801