Exhibit 5.1

Gibson, Dunn & Crutcher LLP

2001 Ross Avenue
Dallas, TX 75201

Tel 214.698.3100

gibsondunn.com

January 25, 2024

Advanced Emissions Solutions, Inc.

8051 E. Maplewood Ave., Suite 210

Greenwood Village, CO 80111

Re: Advanced Emissions Solutions, Inc.
Registration Statement on Form S-3

Ladies and Gentlemen:

We have examined the Registration Statement on Form S-3 (the “Registration Statement”) of Advanced Emissions Solutions, a Delaware corporation (the “Company”), to be filed on the date hereof with the Securities and Exchange Commission (the “Commission”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”), in connection with the registration by the Company for resale from time to time by the selling stockholders identified in the Registration Statement (the “Selling Stockholders”) of (a) up to 11,058,387 shares of the Company’s common stock, par value $0.001 per share (the “Common Stock”), beneficially owned by the Selling Stockholders, 10,732,930 of which are issued and outstanding on the date hereof (the “Outstanding Shares”) and the remainder of which are issuable from time to time upon conversion of the Warrant to Purchase Shares of Common Stock of the Company (the “Warrant”) held by a certain Selling Stockholder as of the date hereof (the “Warrant Shares”), and (b) the associated preferred share purchase rights (the “Rights”), the terms of which are set forth in the Tax Asset Protection Plan, dated as of May 5, 2017, by and between the Company and Computershare Trust Company, N.A., as Rights Agent (as amended through the date hereof, the “TAPP”).

In arriving at the opinions expressed below, we have examined originals, or copies certified or otherwise identified to our satisfaction as being true and complete copies of the originals, of such documents, corporate records, certificates of officers of the Company and of public officials and other instruments as we have deemed necessary or advisable to enable us to render the opinions set forth below. In our examination, we have assumed without independent investigation the genuineness of all signatures, the legal capacity and competency of all natural persons, the authenticity of all documents submitted to us as originals and the conformity to original documents of all documents submitted to us as copies.

Based upon the foregoing, and subject to the assumptions, exceptions, qualifications and limitations set forth herein, we are of the opinion that:

Advanced Emissions Solutions, Inc.

January 25, 2024

Page 2

1.The Outstanding Shares are validly issued, fully paid and non-assessable and the Rights associated with the Outstanding Shares are validly issued.

2.The Warrant Shares, when and if issued from time to time upon conversion of the Warrant in accordance with its terms, and for any additional consideration specified therein, which consideration, on a per-share basis, shall not be less than the par value of the Common Stock, will be validly issued, fully paid and non-assessable and the Rights associated with the Warrant Shares will be validly issued.

With respect to our opinions concerning the Rights, we express no opinion regarding the TAPP or whether or not the Board of Directors of the Company in adopting the TAPP and approving the issuance of the Rights acted in a manner consistent with its fiduciary duties under applicable law and such opinions are based upon the assumption that such adoption and issuance was consistent with such duties. Furthermore, we advise you that the Board of Directors of the Company may be required to redeem or terminate, or take other action with respect to, the Rights at some future time based on the facts and circumstances existing at that time.

A.We render no opinion herein as to matters involving the laws of any jurisdiction other than the Delaware General Corporation Law. This opinion is limited to the effect of the current state of Delaware General Corporation Law and the facts as they currently exist. We assume no obligation to revise or supplement this opinion in the event of future changes in such laws or the interpretations thereof or such facts.

We consent to the filing of this opinion as an exhibit to the Registration Statement, and we further consent to the use of our name under the caption “Legal Matters” in the Registration Statement and the prospectus that forms a part thereof. In giving these consents, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission promulgated thereunder.

Very truly yours,

/s/ Gibson, Dunn & Crutcher LLP