Model order reduction for parameterized partial differential equations is a very active research area that has seen tremendous development in recent years from both theoretical and applica- tion perspectives. A particular promising approach is the reduced basis method that relies on the approximation of the solution manifold of a parameterized system by tailored low dimen- sional approximation spaces that are spanned from suitably selected particular solutions, called snapshots. With speedups that can reach several orders of magnitude, reduced basis methods enable high fidelity real-time simulations for certain problem classes and dramatically reduce the computational costs in many-query applications. While the ”online efficiency” of these model reduction methods is very convincing for problems with a rapid decay of the Kolmogorov n- width, there are still major drawbacks and limitations. Most importantly, the construction of the reduced system in a so called ”offline phase” is extremely CPU-time and memory consuming for large scale or multiscale systems. For practical applications, it is thus necessary to derive model reduction techniques that do not rely on a classical offline/online splitting but allow for more flexibility in the usage of computational resources. In this talk we focus on both, localized training and on-the-fly enrichment strategies for localized model order reduction of multiscale problems in the context of PDE constrained optimization. The approaches are based on the reduced basis - trust region framework. Concepts of rigorous certification and convergence will be presented, as well as numerical experiments that demonstrate the efficiency of the proposed approaches.