  We prove that twisted unions of $L_1$-embedable metric spaces under some very
general assumptions embed into $L_1$ with uniformly bounded distortions. In
particular, the twisted unions of hypercubes studied by Johnson, Lindenstrauss,
and Schechtman, and by Naor and Rabani embed into $L_1$ with bounded
distortion.
  In the second part, we use the theory of stable metric spaces to find simple
examples of metric spaces which are isometric to subsets of $L_p$ $(1\le
p<\infty)$ but embeddings of their unions have distortion at least $3$.
