  Adaptive isogeometric methods for the solution of partial differential
equations rely on the construction of locally refinable spline spaces. A simple
and efficient way to obtain these spaces is to apply the multi-level
construction of hierarchical splines, that can be used on single-patch domains
or in multi-patch domains with $C^0$ continuity across the patch interfaces.
Due to the benefits of higher continuity in isogeometric methods, recent works
investigated the construction of spline spaces with global $C^1$ continuity on
two or more patches. In this paper, we show how these approaches can be
combined with the hierarchical construction to obtain global $C^1$ continuous
hierarchical splines on two-patch domains. A selection of numerical examples is
presented to highlight the features and effectivity of the construction.
