An isolated antibody that binds an extracellular domain of a human SIRP-α polypeptide, wherein the antibody binds the extracellular domain of a human SIRP-α v1 polypeptide, the extracellular domain of a human SIRP-α v2 polypeptide, the extracellular domain of a monkey SIRP-α polypeptide, and the extracellular domain of a murine SIRP-α polypeptide; and wherein the antibody comprises: (a) a heavy chain variable domain comprising: (i) an HVR-H1 sequence comprising the amino acid sequence of X 1 X 2 AX 3 S, wherein X 1 is S or T; X 2 is N, Y, H, or D; and X 3 is M, L, or V (SEQ ID NO:297); (ii) an HVR-H2 sequence comprising the amino acid sequence of GISX 1 X 2 X 3 X 4 X 5 X 6 YYX 7 X 8 SX 9 KG, wherein X 1 is A or S; X 2 is G, S, or absent; X 3 is S, D or G; X 4 is G or S; X 5 is D, S, or G; X 6 is T or A; X 7 is P, G, V, I, A, or S; X 8 is A, D, or G; and X 9 is V or M (SEQ ID NO:298); and (iii) an HVR-H3 sequence comprising the amino acid sequence of ETWNHLFDY (SEQ ID NO:193); and (b) a light chain variable domain comprising: (i) an HVR-L1 sequence comprising the amino acid sequence of SGGX 1 X 2 X 3 SX 4 YYX 5, wherein X 1 is D, G, S, I, or absent; X 2 is S, W, G, Y, D, or absent; X 3 is S, Y, T, or D; X 4 is H, T, S, or Y; and X 5 is G or A (SEQ ID NO:299); (ii) an HVR-L2 sequence comprising the amino acid sequence of SDX 1 X 2 RPX 3, wherein X 1 is D or N; X 2 is E, K, or Q; and X 3 is S or P (SEQ ID NO:300); and (iii) an HVR-L3 sequence comprising the amino acid sequence of X 1 X 2 YDX 3 X 4 X 5 YX 6 NX 7, wherein X 1 is G or A; X 2 is G or A; X 3 is G, Y, Q, S, or A; X 4 is S, R, or T; X 5 is T or S; X 6 is A, I, V, L, or T; and X 7 is T, A, D, or P (SEQ ID NO:301). (a) a heavy chain variable domain comprising: (i) an HVR-H1 sequence comprising the amino acid sequence of X 1 X 2 AX 3 S, wherein X 1 is S or T; X 2 is N, Y, H, or D; and X 3 is M, L, or V (SEQ ID NO:297); (ii) an HVR-H2 sequence comprising the amino acid sequence of GISX 1 X 2 X 3 X 4 X 5 X 6 YYX 7 X 8 SX 9 KG, wherein X 1 is A or S; X 2 is G, S, or absent; X 3 is S, D or G; X 4 is G or S; X 5 is D, S, or G; X 6 is T or A; X 7 is P, G, V, I, A, or S; X 8 is A, D, or G; and X 9 is V or M (SEQ ID NO:298); and (iii) an HVR-H3 sequence comprising the amino acid sequence of ETWNHLFDY (SEQ ID NO:193); and (i) an HVR-H1 sequence comprising the amino acid sequence of X 1 X 2 AX 3 S, wherein X 1 is S or T; X 2 is N, Y, H, or D; and X 3 is M, L, or V (SEQ ID NO:297); (ii) an HVR-H2 sequence comprising the amino acid sequence of GISX 1 X 2 X 3 X 4 X 5 X 6 YYX 7 X 8 SX 9 KG, wherein X 1 is A or S; X 2 is G, S, or absent; X 3 is S, D or G; X 4 is G or S; X 5 is D, S, or G; X 6 is T or A; X 7 is P, G, V, I, A, or S; X 8 is A, D, or G; and X 9 is V or M (SEQ ID NO:298); and (iii) an HVR-H3 sequence comprising the amino acid sequence of ETWNHLFDY (SEQ ID NO:193); and (b) a light chain variable domain comprising: (i) an HVR-L1 sequence comprising the amino acid sequence of SGGX 1 X 2 X 3 SX 4 YYX 5, wherein X 1 is D, G, S, I, or absent; X 2 is S, W, G, Y, D, or absent; X 3 is S, Y, T, or D; X 4 is H, T, S, or Y; and X 5 is G or A (SEQ ID NO:299); (ii) an HVR-L2 sequence comprising the amino acid sequence of SDX 1 X 2 RPX 3, wherein X 1 is D or N; X 2 is E, K, or Q; and X 3 is S or P (SEQ ID NO:300); and (iii) an HVR-L3 sequence comprising the amino acid sequence of X 1 X 2 YDX 3 X 4 X 5 YX 6 NX 7, wherein X 1 is G or A; X 2 is G or A; X 3 is G, Y, Q, S, or A; X 4 is S, R, or T; X 5 is T or S; X 6 is A, I, V, L, or T; and X 7 is T, A, D, or P (SEQ ID NO:301). (i) an HVR-L1 sequence comprising the amino acid sequence of SGGX 1 X 2 X 3 SX 4 YYX 5, wherein X 1 is D, G, S, I, or absent; X 2 is S, W, G, Y, D, or absent; X 3 is S, Y, T, or D; X 4 is H, T, S, or Y; and X 5 is G or A (SEQ ID NO:299); (ii) an HVR-L2 sequence comprising the amino acid sequence of SDX 1 X 2 RPX 3, wherein X 1 is D or N; X 2 is E, K, or Q; and X 3 is S or P (SEQ ID NO:300); and (iii) an HVR-L3 sequence comprising the amino acid sequence of X 1 X 2 YDX 3 X 4 X 5 YX 6 NX 7, wherein X 1 is G or A; X 2 is G or A; X 3 is G, Y, Q, S, or A; X 4 is S, R, or T; X 5 is T or S; X 6 is A, I, V, L, or T; and X 7 is T, A, D, or P (SEQ ID NO:301).