1. Don't confuse estate taxes with income taxes. Estate taxes are paid when a person dies with an estate valued over a certain amount. A person can inherit an asset without paying estate taxes, but the asset would still be subject to applicable income taxes. For example, if you inherit a house, you might still owe taxes when the house is sold.
2. Don't confuse estate tax concerns with probate issues. Estate taxes are paid when a person dies with an estate valued over a certain amount. Probate refers to a process, regulated by your state, of accounting for a deceased person's assets and overseeing distribution to heirs. Thus, if you set up a trust to avoid probate, this would not affect any estate tax implications. (Although a trust can be set up to deal with probate avoidance AND estate tax issues.)
3. Under prior law, a married couple needed a special trust (sometimes called "credit shelter") to take advantage of both spouses' exemption credits and thereby be able to leave a larger estate to heirs tax free. Under current law, a married couple can use both credits without a special trust. This means, effectively, that a married couple can now leave around $10 million in assets to heirs estate tax free. There are different rules for non US citizens.
4. Couples who had taxable estates in prior years (due to a different exemption amount) should have their estate plans reviewed. These outdated estate plans may cause the unnecessary funding of trusts that were designed for different tax rules. As a result, needed assets could be "locked up" in trusts.
5. In prior years, due to different tax rules, it was often important to balance the assets of a married couple so that each spouse owned an equivalent portion of the assets. It is important to re-visit those decisions in light of new tax rules. There may be other reason to title assets in either spouse's name (such as protection from creditors).