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.