Making accurate predictions is a crucial factor in many systems (such as in modelling energy consumption, power load forecasting, traffic networks, process industry, environmental modelling, biomedicine, brain-machine interfaces) for cost savings, efficiency, health, safety and organizational purposes. In this proposal we aim at realizing a new generation of more advanced black-box modelling techniques for estimating predictive models from measured data. We will study different optimization modelling frameworks in order to obtain improved black-box modelling approaches. This will be done by specifying models through constrained optimization problems by studying different candidate core models (parametric models, support vector machines and kernel methods) together with additional sets of constraints and regularization mechanisms. Different candidate mathematical frameworks will be considered with models that possess primal and (Lagrange) dual model representations, functional analysis in reproducing kernel Hilbert spaces, operator splitting and optimization in Banach spaces. Several aspects that are relevant to black-box models will be studied including incorporation of prior knowledge, structured dynamical systems, tensorial data representations, interpretability and sparsity, and general purpose optimization algorithms. The methods should be suitable for handling larger data sets and high dimensional input spaces. The final goal is also to realize a next generation software tool (including symbolic generation of models and handling different supervised and unsupervised learning tasks, static and dynamic systems) that can be generically applied to data from different application areas. The proposal A-DATADRIVE-B aims at getting end-users connected to the more advanced methods through a user-friendly data-driven black-box modelling tool. The methods and tool will be tested in connection to several real-life applications.