A map \(f: X \rightarrow X\) from a metric space \((X,d)\) into another space \((X,d)\) is said to be a bilipschitz embedding if there is a constant \(\lambda\geq 1\) such that \(\lambda^{-1}d(x,y) \leq d(f(x),f(y))\leq\lambda d(x,y),\) for all \(x,y\in X.\) The paper describes some basic geometric tools to construct bilipschitz embeddings of metric spaces into finite-dimensional Euclidean or hyperbolic spaces.