or a pharmaceutically acceptable salt thereof, wherein:

Ring B is a 5-membered heteroaryl ring selected from pyrazole, triazole, or oxadiazole, wherein Ring B is optionally substituted with 0-3 R⁴ groups;

R^Z is halogen, CN, NO₂, or U_(n)R′;

each R¹ is independently halogen, CN, NO₂, or V_(m)R;

V is an optionally substituted C_1-6 alkylidene chain, wherein up to two methylene units of the chain are optionally and independently replaced by —S—, —O—, —CS—, —CO₂—, —OC(O)—, —C(O)—, —C(O)C(O)—, —C(O)NR—, —SO₂NR—, —C(O)NRNR—, —OC(O)NR—, —S(O)—, or —SO₂—;

R² is U_(n)R′;

each occurrence of R⁴ is independently halogen, CN, NO₂, or U_(n)R;

each occurrence of U is independently an optionally substituted C_1-6 alkylidene chain, wherein up to two methylene units of the chain are optionally and independently replaced by —NR—, —S—, —O—, —CS—, —CO₂—, —OC(O)—, —C(O)—, —C(O)C(O)—, —C(O)NR—, —NRC(O)—, —NRCO₂—, —SO₂NR—, —NRSO₂—, —C(O)NRNR—, —NRC(O)NR—, —OC(O)NR—, —NRNR—, —NRSO₂NR—, —S(O)—, or —SO₂—;

m and n are each independently 0 or 1;

each occurrence of R is independently hydrogen or an optionally substituted C_1-6 aliphatic group;

each occurrence of R′ is independently hydrogen or an optionally substituted C_1-6 aliphatic group, a 3-8-membered saturated, partially unsaturated, or fully unsaturated monocyclic ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or an 8-12 membered saturated, partially unsaturated, or fully unsaturated bicyclic ring system having 0-5 heteroatoms independently selected from nitrogen, oxygen, or sulfur; or: R and R′, two occurrences of R, or two occurrences of R′, are taken together with the atom(s) to which they are bound to form an optionally substituted 3-12 membered saturated, partially unsaturated, or fully unsaturated monocyclic or bicyclic ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur;

q is 0, 1, 2, or 3;

each occurrence of R⁶ is independently halogen, CN, NO₂, or U_(n)R′, or: two occurrences of R⁶, or R′ and R⁶, taken together with the atoms to which they are bound, form an optionally substituted 3-6-membered cycloalkyl, heterocyclyl, aryl or heteroaryl ring;

Ar¹ is a 5-8 membered saturated, partially unsaturated, or fully unsaturated monocyclic ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or an 8-12 membered saturated, partially unsaturated, or fully unsaturated bicyclic ring system having 0-5 heteroatoms independently selected from nitrogen, oxygen, or sulfur; wherein Ar¹ is optionally substituted with 0-5 occurrences of TR⁷;

T is a valence bond or is a C₁-C₆ alkylidene chain wherein up to two methylene units of T are optionally and independently replaced by —NR—, —S—, —O—, —CS—, —CO₂—, —OC(O)—, —C(O)—, —C(O)C(O)—, —C(O)NR—, —NRC(O)—, —NRCO₂—, —SO₂NR—, —NRSO₂—, —C(O)NRNR—, —NRC(O)NR—, —OC(O)NR—, —NRNR—, —NRSO₂NR—, —S(O)—, or —SO₂—; and

each occurrence of R⁷ is independently R′, halogen, NO₂, or CN, wherein

optional substituents on an unsaturated carbon of an aryl or heteroaryl group are selected from halogen; R^o; OR^o; SR^o; 1,2-methylene-dioxy; 1,2-ethylenedioxy; phenyl, optionally substituted with R^o; —O(phenyl) optionally substituted with R^o; (CH₂)_1-2(phenyl), optionally substituted with R^o; CH═CH(phenyl), optionally substituted with R^o; NO₂; CN; N(R^o)₂; NR^oC(O)R^o; NR^oC(O)N(R^o)₂; NR^oCO₂R^o; —NR^oNR^oC(O)R^o; NR^oNR^oC(O)N(R^o)₂; NR^oNR^oCO₂R^o; C(O)C(O)R^o; C(O)CH₂C(O)R^o; CO₂R^o; C(O)R^o; C(O)N(R^o)₂; OC(O)N(R^o)₂; S(O)₂R^o; SO₂N(R^o)₂; S(O)R^o; NR^oSO₂N(R^o)₂; NR^oSO₂R^o; C(═S)N(R^o)₂; C(═NH)—N(R^o)₂; or (CH₂)_0-2NHC(O)R^o, wherein each independent occurrence of R^o is selected from hydrogen, optionally substituted C_1-6 aliphatic, an unsubstituted 5-6 membered heteroaryl or heterocyclic ring, phenyl, O(phenyl), or CH₂(phenyl), or, notwithstanding the definition above, two independent occurrences of R^o, on the same substituent or different substituents, taken together with the atom(s) to which each R^o group is bound, form a 3-8 membered cycloalkyl, heterocyclyl, aryl, or heteroaryl ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, wherein optional substituents on the aliphatic group of R^o are selected from NH₂, NH(C_1-4aliphatic), N(C_1-4aliphatic)₂, halogen, C_1-4aliphatic, OH, O(C_1-4aliphatic), NO₂, CN, CO₂H, CO₂(C_1-4aliphatic), O(haloC_1-4 aliphatic), or haloC_1-4aliphatic,

optional substituents on an aliphatic group or on a non-aromatic heterocyclic ring are selected from those defined above for the unsaturated carbon of an aryl or heteroaryl group and the following: ═O, ═S, ═NNHR* ═NN(R*)₂, ═NNHC(O)R* ═NNHCO₂(alkyl), ═NNHSO₂(alkyl), or ═NR* where each R* is independently selected from hydrogen or an optionally substituted C_1-6 aliphatic, wherein substituents on the aliphatic group of R* are selected from NH₂, NH(C_1-4 aliphatic), N(C_1-4 aliphatic)₂, halogen, C_1-4 aliphatic, OH, O(C_1-4 aliphatic), NO₂, CN, CO₂H, CO₂(C_1-4 aliphatic), O(halo C_1-4 aliphatic), or halo(C_1-4 aliphatic), and

optional substituents on the nitrogen of a non-aromatic heterocyclic ring are selected from R⁺, N(R⁺)₂, C(O)R⁺, CO₂R⁺, C(O)C(O)R⁺, C(O)CH₂C(O)R⁺, SO₂R⁺, SO₂N(R⁺)₂, C(═S)N(R⁺)₂, C(═NH)—N(R⁺)₂, or NR⁺SO₂R⁺, wherein R⁺ is hydrogen, an optionally substituted C_1-6 aliphatic, optionally substituted phenyl, optionally substituted O(phenyl), optionally substituted CH₂(phenyl), optionally substituted (CH₂)_1-2(phenyl), optionally substituted CH═CH(phenyl), or an unsubstituted 5-6 membered heteroaryl or heterocyclic ring having one to four heteroatoms independently selected from oxygen, nitrogen, or sulfur, or, notwithstanding the definition above, two independent occurrences of R⁺, on the same substituent or different substituents, taken together with the atom(s) to which each R⁺ group is bound, form a 3-8-membered cycloalkyl, heterocyclyl, aryl, or heteroaryl ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, wherein optional substituents on the aliphatic group or the phenyl ring of R⁺ are selected from NH₂, NH(C_1-4 aliphatic), N(C_1-4 aliphatic)₂, halogen, C_1-4 aliphatic, OH, O(C_1-4 aliphatic), NO₂, CN, CO₂H, CO₂(C_1-4 aliphatic), O(halo C_1-4 aliphatic), or halo(C_1-4 aliphatic).