The trustee of a revocable living trust is responsible for managing the assets within the trust according to the terms set by the grantor (the person who created the trust). This includes investing and distributing assets, paying any debts or taxes owed by the trust, and ensuring that beneficiaries receive their designated inheritance. If the grantor becomes incapacitated, the trustee also steps in to manage the trust's affairs, providing continuity and care in the management of the estate.