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Keyed in multiple places:

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Key to Apiaceae, Key A: Apiaceae with simple leaves

Apiaceae

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1 Leaves linear, lanceolate, or oblanceolate, > 4× as long as wide.
  2 Leaves phyllodial (septate, hollow or flat, segmented); flowers white or purple; [plants of wetlands].
    3 Umbels simple; leaves spatulate, broader towards the tip, often somewhat flattened in ×-section, rounded or obtuse at the apex
    3 Umbels compound; leaves tapering to a pointed tip, either flat or terete in ×-section.
      4 Leaves flat in ×-section, with obvious parallel venation and less obvious septae / cross-partitions
      4 Leaves terete in ×-section, the septae obvious.
        5 Plants 1-11 dm tall, annuals, sometimes mat-forming and adventitiously perennial; fruits 1-3 mm long, with lateral ribs; rays 3-15
        5 Plants 6-24 dm tall, perennials from rhizomes or tubers; fruits 4-9 mm long, with lateral wings; rays 5-20
  2 Leaves “normal” (non-septate, flat, continuous, and in some cases lobed, toothed, or spinose-margined); flowers blue, yellow, white, or whitish-green; [plants of wetlands or uplands].
          6 Flowers borne in involucrate heads; corolla blue or greenish-white
          6 Flowers in compound umbels; corolla yellow or white.
             7 Stem leaves similar to the basal, all simple; corollas yellow; [non-native, of upland disturbed areas]
             7 Stem leaves palmately 3-5-foliolate with linear leaflets, differing from the simple basal leaves; corollas white; [native, of swamps, blackland prairies, and associated disturbed areas, from AL and TN westward]
1 Leaves orbicular, ovate, or elliptic, < 4× as long as wide.
               8 Leaves orbicular, about as wide as, or wider than, long; base peltate or cordate.
                 9 Leaves leathery, with spinose margins; inflorescence a head; flowers blue; [rare introduction]
                 9 Leaves herbaceous or somewhat fleshy. toothed or lobed, but not spinose; inflorescence umbellate or verticillate; flowers white, greenish, or purplish; [collectively common and widespread].
                   10 Foliage and fruits (or ovaries) glabrous; leaves toothed, sometimes also lobed; [common natives and exotics]
               8 Leaves ovate or elliptic, 1.2-4× as wide as long; base cordate, peltate, or truncate.
(c) Fleming, Gary P.
                     11 Leaves perfoliate; flowers yellow; [rare exotics].
                     11 Leaves cordate or truncate at the base; flowers white, green, yellow, blue, or purple;
                          13 Flowers greenish or blue; leaves all simple (sometimes stem leaves lobed); inflorescence a head or very congested (subcapitate) umbel; [plants of wetland situations, prostrate, creeping, or erect].
                            14 Inflorescence a very congested (subcapitate) umbel, with 4-9 flowers; leaves cordate at the base, long-petiolate, the petioles characteristically 2× as long as the leaf
                            14 Inflorescence a head, with > 20 flowers; leaves cuneate to truncate at the base, sessile to short petiolate, the petioles < 1× as long as the leaf (except E. prostratum)
                          13 Flowers yellow or purple; basal leaves simple, stem leaves usually compound; Inflorescence a compound umbel; [erect plants of upland situations].
                              15 Fruits (partly to fully mature) with thin-edged wings; flowers yellow or purple; central flower of each umbellet staminate and pedicelled; fruits all pedicelled in all umbellets
                              15 Fruits ribbed (with rounded, cordlike ribs), lacking thin-edged wings; flowers yellow; central flower of each umbellet either staminate and pedicelled, or pistillate and sessile; fruits all pedicelled in some umbellets (those with a staminate central flower), or the central fruit sessile in some umbellets (those with a pistillate central flower)
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Key to Apiaceae, Key D: Apiaceae with leaves 2-4× pinnately-ternately compound, the ultimate leaflets distinct and relatively broad

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  2 Leaflets broad, elliptic, ovate, or obovate, sparingly lobed; corolla yellow
1 Leaflets variously serrate, dentate, and/or incised.
    3 Plants in flower.
      4 Corolla yellow, maroon, pale creamy yellow, or yellowish green.
        5 Herbs acaulescent to short-caulescent, 1-4 dm tall; [endemic to se. TX]
        5 Herbs caulescent, 1.8-15 dm tall; [east and north of se. TX or rare garden escape].
          6 Plants annual; foliage aromatic when crushed; [rare garden escape]
          6 Plants perennial; foliage odorless or foul-smelling (Zizia) when crushed; [native species].
             7 Flowers yellow, maroon, or pale creamy-yellow; central flower of each umbellet staminate and pedicelled; fruits all pedicelled in all umbellets; developing fruits subterete to slightly dorsally compressed, several or all of the ribs with thin-edged wings
             7 Flowers yellow; central flower of each umbellet either staminate and pedicelled, or pistillate and sessile; fruits all pedicelled in some umbellets (those with a staminate central flower), or the central fruit sessile in some umbellets (those with a pistillate central flower); developing fruits laterally compressed, all of the ribs rounded and cordlike
                 9 Rays 16-25; leaves somewhat coriaceous; leaflet bases often cuneate or obliquely truncate; [plants of dry habitats]
                 9 Rays 3-5; leaves thin in texture; leaflet bases rounded, subcordate, or broadly cuneate; [plants of moist forests]
                   10 Basal leaves lobed or 1-pinnate, cauline leaves ternate and narrowing upward [rare native in nw. LA, OK, and c. TX]
                   10 Basal leaves ternate and similar to cauline leaves; [either rarely naturalized non-natives or more widespread natives]
                     11 Plants 1-12 dm tall at maturity; [either naturalized non-natives or uncommon native species in OK or TX].
                       12 Plants to 4 dm tall; acaulescent; [uncommon native species in OK and TX]
                          13 Involucel bractlets relatively small, not showy, green or purplish, herbaceous, not enveloping young umbellets
                          13 Involucel bractlets large, showy, green or purple with broad white margins, usually scarious, enveloping young umbellets
                       12 Plants to 12 dm tall; caulescent; [naturalized non-natives]
                            14 Ovary (and later the fruits) terete, the ribs corky-winged; [plants of wetlands]
                            14 Ovary (and later the fruits) laterally compressed, not winged; [plants of uplands]
                              15 Umbellets (rays) (25-) 50-100 per umbel; [primarily southern and western portions of the FSUS region]
                     11 Plants 6-18 dm tall at maturity; [collectively common and widespread natives].
(c) Gilliam, Stan
                                16 Sheaths of the upper leaves dilated, > 1 cm wide when flattened; [plants of moist habitats, from GA northward in the Mountains, extending into adjacent provinces towards the northern edge of our area]
                                16 Sheaths of the upper leaves not dilated, < 1 cm wide; [plants either of wetlands or of moist to dry forests].
                                  17 Veins of the leaflets directed to the sinuses; leaflets mostly 2.5-5× as long as wide, acuminate at the tip; [of wetlands]
                                  17 Veins of the leaflets directed to the tips of the teeth or lobes; leaflets mostly 1.3-1.8× as long as wide, acute to obtuse at the tip; [of moist to dry forests]
    3 Plants in fruit.
                                       19 Fruits 4-6 mm long, hispid across the surfaces; rays 16-25; leaves somewhat coriaceous; leaflet bases often cuneate or obliquely truncate; [plants of dry habitats]
                                       19 Fruits 18-24 mm long, oblanceolate or linear, appressed-pubescent on the ribs; rays 3-5; leaves thin in texture; leaflet bases rounded, subcordate, or broadly cuneate; [plants of moist forests]
                                           21 Fruits strongly dorsiventrally compressed, ovate to oblong 4.5-12 mm long, strongly winged; [north of se. TX]
                                         20 Herbs caulescent, 1.8-15 dm tall; [more widespread, mostly eastward or garden escape]
                                               23 Fruits dorsally compressed (strongly to slightly) or subterete, either thin-winged or corky-winged.
                                                 24 Basal leaves ternate and similar to cauline leaves; [rarely naturalized non-natives or more widespread natives]
                                                    25 Ribs thin-winged; fruits 3-8 mm long; [common natives of most to submesic forests].
                                                      26 Rays 12-30; fruits 4-8 mm long; plant 6-20 dm tall; sheaths of the upper leaves dilated, > 1 cm wide when flattened
                                                      26 Rays 5-10; fruits 3-6 mm long; plant 5-10 dm tall; sheaths of the upper leaves not dilated, < 1 cm wide
                                                        27 Veins of the leaflets either directed to the tips of the teeth or lobes, or reticulating extensively and becoming obscure before reaching the margin; leaflets mostly 1.3-1.8× as long as wide, acute to obtuse at the tip; [of moist to dry forests or disturbed areas].
                                                            29 Plants perennial or Ammi majus annual; foliage odorless or foul-smelling (Zizia) when crushed; [native or naturalized species].
                                                              30 Lateral veins of the leaflet arcing, reticulating and becoming obscure before reaching the leaflet margin; leaflet base symmetrical or slightly oblique; leaflet margin toothed to or very close to the base
                                                                 31 Umbellets (rays) per umbel 4-25