1. A bispecific binding protein that binds to PD-1 and CTLA-4 comprising a first heavy chain comprising the amino acid sequence of SEQ ID NO: 9, a first light chain comprising the amino acid sequence of SEQ ID NO: 7, a second heavy chain comprising the amino acid sequence of SEQ ID NO: 12, and a second light chain comprising the amino acid sequence of SEQ ID NO: 4.

13. A bispecific binding protein that binds to PD-1 and CTLA-4 comprising: (i) a first heavy chain comprising a VH1-CDR1, VH1-CDR2 and VH1-CDR3, wherein VH1-CDR1 comprises the amino acid sequence of residues 26-35 of SEQ ID NO: 9, wherein VH1-CDR2 comprises the amino acid sequence of residues 50-66 of SEQ ID NO: 9, and wherein VH1-CDR3 comprises the amino acid sequence of residues 99-111 of SEQ ID NO: 9; (ii) a first light chain comprising a VL1-CDR1, VL1-CDR2, VL1-CDR3, wherein VL1-CDR1 comprises the amino acid sequence of residues 24-41 of SEQ ID NO: 7, wherein VL1-CDR2 comprises the amino acid sequence of residues 55-61 of SEQ ID NO: 7, and wherein VL1-CDR3 comprises the amino acid sequence of residues 94-100 of SEQ ID NO: 7; (iii) a second heavy chain comprising a VH2-CDR1, VH2-CDR2 and VH2-CDR3, wherein VH2-CDR1 comprises the amino acid sequence of residues 26-35 of SEQ ID NO: 12, wherein VH2-CDR2 comprises the amino acid sequence of residues 50-66 of SEQ ID NO: 12, and wherein VH2-CDR3 comprises the amino acid sequence of residues 99-114 of SEQ ID NO: 12; and (iv) a second light chain comprising a VL2-CDR1, VL2-CDR2 and VL2-CDR3, wherein VL2-CDR1 comprises the amino acid sequence of residues 24-34 of SEQ ID NO: 4, wherein VL2-CDR2 comprises the amino acid sequence of residues 50-56 of SEQ ID NO: 4, and wherein VL2-CDR3 comprises the amino acid sequence of residues 89-95 of SEQ ID NO: 4.

14. The protein of claim 13 comprising an Fc region, wherein the Fc region is aglycosylated.

15. The protein of claim 13 comprising an Fc region, wherein the Fc region is deglycosylated.

16. The protein of claim 13 comprising an Fc region, wherein the Fc region has reduced fucosylation or is afucosylated.

17. A composition comprising the protein of claim 13 and a pharmaceutically acceptable carrier.

18. A nucleic acid molecule comprising a nucleotide sequence encoding a protein of claim 13.

19. A vector comprising the nucleic acid molecule of claim 18.

20. An isolated host cell comprising the vector of claim 19.

21. A method of treating cancer in a subject, the method comprising administering the protein of claim 13 to the subject.

22. The method of claim 21, wherein the cancer is one or more of ovarian cancer, breast cancer, colorectal cancer, prostate cancer, cervical cancer, uterine cancer, testicular cancer, bladder cancer, head and neck cancer, melanoma, pancreatic cancer, renal cell carcinoma, and lung cancer.

23. A method of enhancing an immune response in a subject, the method comprising administering the protein of claim 13 to the subject.

24. A bispecific binding protein that binds to PD-1 and CTLA-4 comprising a first heavy chain variable region comprising the amino acid sequence of SEQ ID NO: 51, a first light chain variable region comprising the amino acid sequence of SEQ ID NO: 49, a second heavy chain variable region comprising the amino acid sequence of SEQ ID NO: 52, and a second light chain variable region comprising the amino acid sequence of SEQ ID NO: 54.

25. The protein of claim 24 comprising an Fc region, wherein the Fc region is aglycosylated.

26. The protein of claim 24 comprising an Fc region, wherein the Fc region is deglycosylated.

27. The protein of claim 24 comprising an Fc region, wherein the Fc region has reduced fucosylation or is afucosylated.

28. A composition comprising the protein of claim 24 and a pharmaceutically acceptable carrier.

29. A nucleic acid molecule comprising a nucleotide sequence encoding a protein of claim 24.

30. A vector comprising the nucleic acid molecule of claim 29.

31. An isolated host cell comprising the vector of claim 30.

32. A method of treating cancer in a subject, the method comprising administering the protein of claim 24 to the subject.

33. The method of claim 32, wherein the cancer is one or more of ovarian cancer, breast cancer, colorectal cancer, prostate cancer, cervical cancer, uterine cancer, testicular cancer, bladder cancer, head and neck cancer, melanoma, pancreatic cancer, renal cell carcinoma, and lung cancer.

34. A method of enhancing an immune response in a subject, the method comprising administering the protein of claim 24 to the subject.

35. The method of claim 10, wherein the cancer is melanoma.

36. The method of claim 10, wherein the cancer is renal cell carcinoma.

37. The method of claim 10, wherein the cancer is lung cancer.

38. The method of claim 22, wherein the cancer is melanoma.

39. The method of claim 22, wherein the cancer is renal cell carcinoma.

40. The method of claim 22, wherein the cancer is lung cancer.

41. The method of claim 33, wherein the cancer is melanoma.

42. The method of claim 33, wherein the cancer is renal cell carcinoma.

43. The method of claim 33, wherein the cancer is lung cancer.