The trustee of a trust is the person who title to property has been transferred to so they can manage and administer it pursuant to the terms of the trust. The selection of trustee or co-trustees can be an important one.
A trust can have one or more trustees. In the typical married couple "probate avoidance" revocable living trust, the husband and wife are typically the initial co-trustees. Their powers to act jointly or individually may be described in the trust instrument. In the single person trust, typically that single person is the initial trustee.
Who can be a trustee? A trustee "can" be, generally, an individual, a bank, or a trust company. But in the Mom and Pop revocable living trust, typically the trustees are one or more individuals.
There are typically successor or backup trustees named. When Mom and Pop set up a revocable trust, they typically name themselves as the initial co-trustees. Then, after Mom and Pop die, one or more of the adult children are named as the Successor Trustee or Co-Trustees.
Trusts often provide a default provision so that if none of the named trustees can serve as trustee, then a corporate trustee gets appointed to serve as trustee. But that's only in the even that none of the named initial or successor trustees can or won't serve.