Theme: Chin up, bucko - No need to abandon all hope ye who enter here, so long as you parse 37-Across as AB and ON.
37. Leave high and dry ... or, when divided into three parts, what the answers to starred clues are encompassed by: ABANDON. AB-AND-ON
16. *Bath towel material: ABSORBENT COTTON
22. *Bart and Lisa's grandpa: ABE SIMPSON
49. *"Falcon Crest" actress: ABBY DALTON
59. *Book that's been shortened: ABRIDGED VERSION
Argyle here with our fearless leader. Two grid spanners and a couple long climbers are practically her signature.
1. Accessory for Supergirl: CAPE
5. Volkswagen Routan, for one: VAN. Model years: 2009–2014
8. Put into words: SAID
12. Andes animal: LLAMA. The Andes Mountains are the longest and one of the highest mountain ranges in the world. They are located in South America and stretch 4,500 miles from north to south, along the west coast of the continent.
14. Belgrade native: SERB
15. Pinnacle: ACME
19. Pilates class need: MAT
20. Note from the boss: MEMO
21. Data storage media: DISKS
26. Washroom bowls: BASINS
28. "People are saying ... ": "RUMOR IS ... "
32. Saudi's neighbor: OMANI
33. Neeson of the "Taken" films: LIAM
35. Rare Hawaiian goose: NENE. The Hawaiian name nēnē comes from its soft call.
36. Huff Post owner: AOL. The Huffington Post. AOL acquired the Huff Post in 2011.
40. One of a golfer's pocketful: TEE
41. Mex. ladies: SRAs. (señora)
43. Loosen, as laces: UNDO
44. Spew lava and ash: ERUPT
46. Online live-stream lecture: TED TALK. TED(Technology, Entertainment, Design)
48. __ Rico: PUERTO
52. "Haven't the foggiest": "GOT ME"
55. "It's __": "Nobody wins": A TIE
56. Cookie fruit: FIG
63. Male with a thick mane: LION
64. Totals: ADDS
65. "Yes and no": "SORTA"
66. Bluesy James: ETTA
67. Believe, as a story: BUY
68. Tuckered out: BEAT
1. Chowder ingredient: CLAM
2. Jessica of "Good Luck Chuck": ALBA. A fish monger?
3. Picnic side dish: PASTA SALAD
4. Revealing rock genre: EMO
5. Scorpion's poison: VENOM
6. Gallery showing: ART
7. "The Voice" network: NBC
8. Audited, as a class: SAT IN ON
9. Circus performances: ACTs
10. "Everything's fine": "I'M OK"
11. Many man caves: DENS
13. Country south of Georgia: ARMENIA
14. 18-wheeler: SEMI
17. "Porgy and __": BESS
18. Former NBA forward Lamar: ODOM
23. Coal holder: BIN
24. Museum with a Goya Gate: PRADO. Puerta de Goya (Goya Gate), at Prado Museum's north façade, features statue of famed painter outside.
25. Sport with silk-clad referees called gyoji: SUMO
26. Brag: BOAST
27. Love, to Casanova: AMORE
29. Shoot back: RETURN FIRE
30. Ham-handed: INEPT
31. Take care of: SEE TO
33. Tall and lean: LANKY
34. Gary's st.: IND. (Indiana)
38. Onion or shallot: BULB
39. Fixes, as Fido: NEUTERS
42. Mountain climber's need: STAMINA. This had me thinking of equipment. I blame it on PITON from the other day.
45. Rock's __ Speedwagon: REO
47. Still in the sack: ABED. A word, sorry.
48. Ballet knee bend: PLIE
50. Papa: DADDY
51. Off-road rides: Abbr.: ATVs. (all-terrain vehicle)
52. Wind warning indicated by two red flags: GALE
53. "In memoriam" piece: OBIT
54. Relaxed gait: TROT
57. Bitty bit: IOTA
58. Bitty biter: GNAT
60. Shoot the breeze: GAB
61. Academic URL ending: .EDU
62. Have a good cry: SOB