Exhibit 5.1 and 23.1

OPINION OF DAVIS POLK & WARDWELL LLP

August 8, 2016

TerraVia Holdings, Inc.

225 Gateway Boulevard

South San Francisco, CA 94080

Ladies and Gentlemen:

We have acted as special counsel for TerraVia Holdings, Inc., a Delaware corporation (the “Company”), in connection with the issuance and sale by the Company of shares (the “Securities”) of common stock of the Company, par value $0.001 per share (the “Common Stock”), having an aggregate offering price to the public of up to $25,000,000, pursuant to the Company’s Registration Statement on Form S-3 (File No. 333-212448) filed on July 8, 2016 and declared effective by the Securities and Exchange Commission on August 5, 2016 (the “Registration Statement”), a base prospectus and related prospectus supplement dated August 8, 2016 (the “Prospectus Supplement”), and that certain Sales Agreement dated August 8, 2016 (the “Sales Agreement”) by and between the Company and Cowen and Company, LLC.

We, as your counsel, have examined originals or copies of such documents, corporate records, certificates of public officials and other instruments as we have deemed necessary or advisable for the purpose of rendering this opinion.

In rendering the opinion expressed herein, we have, without independent inquiry or investigation, assumed that (i) all documents submitted to us as originals are authentic and complete, (ii) all documents submitted to us as copies conform to authentic, complete originals, (iii) all signatures on all documents that we reviewed are genuine, (iv) all natural persons executing documents had and have the legal capacity to do so, (v) all statements in certificates of public officials and officers of the Company that we reviewed were and are accurate and (vi) all representations made by the Company as to matters of fact in the documents that we reviewed were and are accurate.

Based upon the foregoing, and subject to the additional assumptions and qualifications set forth below, we advise you that, in our opinion, when the Securities have been issued and delivered against payment therefor in accordance with the terms of the Sales Agreement, the Securities will be validly issued, fully paid and non-assessable. In rendering the foregoing opinion, we have assumed that upon the issuance of any of the Securities, the total number of shares of Common Stock issued and outstanding will not exceed the total number of shares of Common Stock that the Company is then authorized to issue under its Amended and Restated Certificate of Incorporation, as amended.

We are members of the Bars of the States of New York and California and the foregoing opinion is limited to the laws of the State of New York and the General Corporation Law of the State of Delaware.

We hereby consent to the filing of this opinion as an exhibit to a report on Form 8-K to be filed by the Company on the date hereof and its incorporation by reference into the Registration Statement and further consent to the reference to our name under the caption “Legal Matters” in the Prospectus Supplement, which is a part of the Registration Statement. In giving this consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act of 1933, as amended.

Very truly yours,

/s/ Davis Polk & Wardwell LLP