In this survey talk, we will discuss several mostly recent results on embeddings of simplicial complexes into the Euclidean space and into manifolds. We will mainly focus on the algorithmic aspects of this question. However, we will also touch few theoretical results. The talk will be based on joint works with Jirka Matoušek and also with Xavier Goaoc, Isaac Mabillard, Pavel Paták, Zuzana Patáková, Eric Sedgwick and Uli Wagner.