I will start by formulating the embedding problem in
topological dynamics as well as presenting its history. Next I will
explore a connection to the notion of Rokhlin dimension which arose in
the context of classification of transformation group $C^*$-algebras,
and provide a new embedding result by a simple and conceptually
appealing proof. Last but not least I will show how the embedding
theorem relates to the celebrated Takens' theorem which has extensive
applications in experimental sciences. We will present a generalized
Takens' theorem for the setting of $\mathbb{Z}^k$-actions and a
continuous observable. This is a joint work with Yonatan Gutman and
Gábor Szabó.