Exhibit 5.1

August 4, 2021

Robinhood Markets, Inc.

Registration Statement on Form S-1

Ladies and Gentlemen:

    We have acted as counsel for Robinhood Markets, Inc., a Delaware corporation (the “Company”), in connection with the registration statement on Form S-1(the “Registration Statement”), filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), for the purpose of registering, under the Securities Act, the resale of an aggregate of up to 97,876,033 shares of the Company’s Class A common stock, par value $0.0001 per share (the “Shares”). The shares are to be offered and sold by the selling stockholders identified in the Registration Statement (the “Selling Stockholders”).

    In that connection, we have examined originals, or copies certified or otherwise identified to our satisfaction, of such documents, corporate records and other instruments as we have deemed necessary or appropriate for the purposes of this opinion, including, without limitation: (a) the Amended and Restated Certificate of Incorporation of the Company, as amended; (b) the Amended and Restated By-laws of the Company, as amended; and (c) certain resolutions adopted by the Board of Directors of the Company.

    In rendering our opinion, we have assumed the genuineness of all signatures, the legal capacity of all natural persons, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as certified, conformed or photostatic copies and the authenticity of the originals of such latter documents. As to all questions of fact material to this opinion that have not been independently established, we have relied upon certificates or comparable documents of officers and representatives of the Company.

    Based on the foregoing and in reliance thereon, we are of the opinion that the Shares have been duly and validly authorized and are validly issued, fully paid and non-assessable.

    We are admitted to practice in the State of New York, and we express no opinion as to matters governed by any laws other than the laws of the State of New York, the General Corporation Law of the State of Delaware and the Federal laws of the United States of America. The reference and limitation to “Delaware General Corporation Law” includes the statutory provisions and all applicable provisions of the Delaware Constitution and reported judicial decisions interpreting these laws.

    We hereby consent to the filing of this opinion with the Commission as Exhibit 5.1 to the Registration Statement. We also consent to the reference to our firm under the caption “Legal matters” in the Registration Statement. In giving this consent, we do not thereby admit that we are included in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission.

Very truly yours,

/s/ Cravath, Swaine & Moore LLP

Robinhood Markets, Inc.

85 Willow Road

Menlo Park, California 94025

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