  Dendroidal sets offer a formalism for the study of $\infty$-operads akin to
the formalism of $\infty$-categories by means of simplicial sets. We present
here an account of the current state of the theory while placing it in the
context of the ideas that lead to the conception of dendroidal sets. We briefly
illustrate how the added flexibility embodied in $\infty$-operads can be used
in the study of $A_{\infty}$-spaces and weak $n$-categories in a way that
cannot be realized using strict operads.
