Dynamical processes in the atmosphere and ocean are central in determining the large-scale drivers of regional climate change, yet predictive understanding of climate dynamics is poor. In this perspective article, we identify three frontline problems in climate dynamics, in which progress is possible, and which will lead to improved predictions and projections and more robust information for climate change adaptation. These problems involve (i) the response to external forcing of storms, blocks and jet streams, (ii) ocean-basin to ocean-basin and tropical-extratropical teleconnections and (iii) the development of predictive theories of climate dynamics involving non-linear interactions between the dynamics and physics of the atmosphere and ocean. We highlight opportunities and techniques for making immediate progress in climate dynamics, namely the development of high-resolution coupled model simulations, partial coupling or pacemaker experiments and the development and use of dynamical metrics and dynamical hierarchies of models. Our particular focus is on the role of the ocean in providing a slowly-evolving boundary condition, and its coupling and interaction with the atmosphere, that plays a central role in driving internal climate variability and in modulating forced climate change.