Glad you asked! Here is an example of a cryptic crossword.
Across
1. Lady losing head for man (4)
3. Sink back to bottom and be covered by extensive dirt surfaces (5)
9. To a larger extent, gritty city with famous zoo keeper finally replacing a couple of gorillas (7)
11. Cool croc oddly made a fashion designer (4)
12. One foot near the stern (3)
15. Rip us off producing hybrid vehicle (5)
17. Beginning driver not starting to become one that makes money (6)
18. Human resources obtaining advantage for investor (6)
19. Wader boots, in Senegal, primarily seen after fourth of April (4)
21. Dry debate about plush toy (5,4)
25. Hands swapped by legitimate ruler in literature (4)
27. Head of brewers nowhere to be seen? English and German brewery product becoming increasingly bizarre (6)
29. Almost sounds like opening back wound (6)
32. Unbeliever rejecting drugs being consumed (5)
34. Poem, essentially including a bit of devotion (3)
35. Aching desire personified, taken the wrong way (4)
36. Confiscation of uniform during unexpected resize (7)
37. European's son smoked weed (5)
38. Attractive man's small earring (4)
Down
1. Promptly like a top pony (4, abbr.)
2. Article by Time describing Queen, perhaps (3)
4. Administer resistance-measuring instrument (5)
5. Woman's brother has one daughter (5)
6. Kind of blue, like this clue (4)
7. Large knife cut, from the top and bottom, removing small part of tendon, leading to pain (4)
8. Oscar developed fierce character, ultimately becoming more harsh (7)
10. Man shoveled in audition (4)
11. Pole dancer's foot that is held under copper (5)
13. Worry about guitar part (4)
14. American man is employed (4)
16. Wide awake entertaining thought (4)
18. Horrible hotels seen all around American island once filled with immigrants (7)
20. Flyer catching one lure (4)
22. Doctor I have to hit with force (5)
23. Contests to be essenceless, without content? (4)
24. Grass-eater looking up to grass (4)
26. Group of Nazis interrupting American writer (5)
27. Finished wanting information, at first? Strange indeed (5)
28. Paparazzis holding a game of 38 across (4)
30. Many a person's sense of self goes bad (4)
31. Disease causes marks on skin with loss of vitamin (4, abbr.)
33. Requirement to massage in audition (4)
34. Reveal orientation of objects under tree tops (3)
