Is it true trusts avoid taxes?

Some do and some don't! There are many different types of trusts.  Some are designed to avoid taxes (life insurance trusts, intentionally defective grantor trusts- an IDGT, qualified personal residence trusts --a QPRT, charitable trusts--CRTs and others), while others are designed for probate avoidance and management of assets (the classical revocable or living trust). In choosing to use a trust for any of your planning needs there are many considerations to be reviewed.  Trusts are great arrows to have in your estate planning quiver so be sure to discuss them with your advisor.