Provided are compositions and methods for prophylaxis and/or therapy of a variety of cancers which express a NY-ESO-1 antigen. Included are recombinant T cell receptors (TCRs), polynucleotides encoding them, expression vectors that include the polynucleotides, and cells into which the polynucleotides have been introduced to produce modified cells, including CD4+ T cells, CD8+ T cells, natural killer T cells, γδ T cells, and progenitor cells, such as haematopoietic stem cells. The modified cells are capable of direct recognition of a cancer cell expressing a NY-ESO-1 antigen by human leukocyte antigen (HLA) class II-restricted binding of the TCR to the NY-ESO-1 antigen expressed by the cancer cell without presentation of the antigen by antigen presenting cells. In embodiments, the NY-ESO-1 antigen is displayed by the tumor cells. Also included is a method for prophylaxis and/or therapy of cancer by administering modified cells that express a recombinant TCR. Methods for making expression vectors and/or cells which express a recombinant TCR and identifying TCRs to make the expression vectors are also included.