A Board of Directors has no legal responsibility identified in ERISA.  As a matter of corporate law, they may ratify the adoption of a Plan, just as Trustees of a Union may ratify adoption of a Plan.  Every employee benefit plan has a Plan document which governs the Plan and every document, hence every plan must specify a “Named Fiduciary” (a 402(a) Fiduciary, (often mistakenly referred to as a 3(21) Fiduciary–see below)).
The Named Fiduciary is usually the Plan Sponsor (generally the employer as an entity).  It is the Named Fiduciary that bears all responsibility (and liability ) for all the activities of a Plan.  Note they can delegate some of the responsibilities to other parties, (but don’t have to).  Still the Named Fiduciary retains liability for prudently selecting a party they delegate responsibility to.
So, the schematic looks like this:
1. The 402(a) Named Fiduciary has ALL responsibility for the administration and investments of a Plan.  This where the proverbial buck stops.  Generally the named Fiduciary is the Plan Sponsor.  In a corporation this is generally the employer.  NOTE in multiple employer Plans (MEPs) there is an outside Named Fiduciary, not the participating employer.  Also note that a few (very few) investment firms will accept being appointed the Named Fiduciary and do everything for the employer.
2. Responsibility for the day to day discretionary portfolio management can be delegated by the Named Fiduciary to a 3(38) Fiduciary (an investment manager with discretion).  In this case there is a safe harbor for the Named Fiduciary with respect to the day-to-day portfolio management, BUT the Named Fiduciary is still responsible (and liable) for the prudent selection.
3. A Named Fiduciary can hire a Directed Trustee, like a Bank or a lawyer, to handle some of the contracting and administration.  A directed Trustee only follows directions, and is generally not a fiduciary.
4. Alternatively, the Named Fiduciary can hire a Discretionary Trustee (uncommon) who then becomes responsible for all administration and investments, with the power to further delegate.
5. The Named Fiduciary can hire a Plan Administration firm as a 3(16) Fiduciary with the discretion to handle all Plan administration.
6. Alternatively, the Named Fiduciary can delegate some Administration to a Third Party Administrator (TPA).  Generally TPAs will NOT accept discretion or acknowledge that they are a fiduciary (Some court cases are overturning that idea, under the legal principle of “Functional Fiduciary” –  Even attorneys and accountants and actuaries are being drawn in by this principle).
7. The Named Fiduciary can purchase from or hire an investment advisor to provide non-discretionary invest advice in the form of recommendations as a 3(21) Fiduciary.  The named fiduciary will retain the discretion and the decision to implement a recommendation or not stays with the Named Fiduciary, not with a 3(21) Fiduciary.
8. The Plan may have an Investment Committee; if they do not hire a 3(38) but the power and responsibility to make investment decisions remains with the named Fiduciary.  The committee functions like a 3(21) Fiduciary.  The Named Fiduciary cannot delegate away its fiduciary responsibility, so, in the case of the Plan Sponsor delegating investment discretion to an investment committee composed of members of the fir, it is like delegating to oneself.  Use of third party administrators and 3(21) Fiduciaries does not (and cannot) mitigate Plan Sponsor liability, if the Sponsor is the Named Fiduciary.
9. Employee Benefit investment committees or “Retirement Committees“, if they exist generally function without discretion.  Such committees will be appointed by the Named Fiduciary,  Appointing an investment committee or not is often used of evidence as a prudent process, but in practice has provided little actual protection from the personal liability associated with fiduciary responsibility.
There may be other wheels that turn, but functionally this includes all the decision tree.