Online Etymology Dictionary

underage (adj.): also under-age, 1590s, from under + age.
underarm (adj.): 1816, "underhand" (in reference to a style of throwing), from under + arm (n.1). First attested 1908 in dressmaking sense of "seams on the lower half of the arm-hole;" as a euphemism for armpit, it is attested from 1930s, popularized by advertisers.
underbelly (n.): c.1600, from under + belly (n.). In figurative sense of "most vulnerable part" it is recorded from Churchill's 1942 speech. Sometimes used erroneously in sense of "seamy or sordid part" of anything.
underbred (adj.): "of inferior breeding, vulgar," 1640s, from under + past participle of breed (v.). Of animals, "not pure bred," attested from 1890.
underbrush (n.): "shrub and small trees in a forest," 1775, from under + brush (n.2). Originally American English; cf. undergrowth, attested in the same sense from 1600.
undercarriage (n.): 1794, from under + carriage. Meaning "landing gear of an aircraft" is recorded from 1911.
underclass (n.): "subordinate social class," 1894, from under (adj.) + class (n.). A loan-translation of Swedish underklass.
underclassman (n.): "sophomore or freshman," 1869, American English, from under (adj.) + class (n.) in the school form sense + man (n.).
undercover (adj.): 1854, "sheltered," from under + cover (n.). Sense of "operating secretly" attested from 1920.
undercroft (n.): "crypt of a church; underground vault," late 14c., from under + croft.
undercurrent (n.): 1660s, "stream of water or air flowing beneath the surface or beneath another current," a hybrid formed from under + current (n.). The figurative sense of "suppressed or underlying character" is attested from 1817.
undercut (v.): late 14c., "to cut down or off," from under + cut (v.). In the commercial sense of "to sell at lower prices" (or work at lower wages) it is first attested 1884. Figurative sense of "render unstable, undermine" is recorded from 1955, from earlier literal meaning "cut so as to leave the upper portion larger than the lower" (1874).
underdeveloped (adj.): 1892, in the photography sense, under + past participle of develop. In reference to countries or regions, recorded from 1949.
underdog (n.): "the beaten dog in a fight," 1887, from under + dog (n.). Cf. top dog "dominant person in a situation or hierarchy."
I'm a poor underdog
But tonight I will bark
With the great Overdog
That romps through the dark.

[from "Canis Major," Robert Frost, 1928]
underdone (adj.): 1680s, in reference to cooked meat, from under + done.
underdressed (adj.): also under-dressed, "too plainly dressed," 1759, from under (adv.) + past participle of dress (v.).
underestimate (v.): 1812, "to estimate at too low an amount," from under + estimate (v.). Meaning "to rank too low, undervalue" is recorded from 1850. Related: Underestimated; underestimating.
underfoot (adv.): c.1200, underfot "under the feet," from under + foot. Cf. Middle Dutch ondervoete. As an adj., attested from 1590s; in reference to persons, "continually in the way," it is recorded from 1891.
undergird (v.): 1520s, from under + gird (v.). Related: Undergirded; undergirding.
undergo (v.): Old English undergan "undermine," from under + gan (see go). Cf. Middle Dutch ondergaen, Old High German untarkun, German untergehen, Danish undergaa. Sense of "submit to, endure" is attested from c.1300. Meaning "to pass through" (an alteration, etc.) is attested from 1630s. Related: Undergone; underwent.
undergrad (n.): short for undergraduate, 1827.
undergraduate (n.): 1620s, a hybrid formed from under + graduate (n.). British used fem. form undergraduette in 1920s-30s.
underground (adv.): 1570s, "below the surface," from under + ground (n.). As an adjective, attested from c.1600; figurative sense of "hidden, secret" is attested from 1630s; adjectival meaning "subculture" is from 1953, from World War II application to resistance movements against German occupation, on analogy of the dominant culture and Nazis. Noun sense of "underground railway" is from 1887 (shortened from phrase underground railway, itself attested from 1834).
Underground Railroad (n.): "network of U.S. anti-slavery activists helping runaways elude capture," attested from 1847, but said to date from 1831 and to have been coined in jest by bewildered trackers after their slaves vanished without a trace. Originally mostly the term for escape networks in the (then) western states of the U.S.
undergrowth (n.): c.1600, from under + growth.
underhand (adv.): Old English under hand "in subjection," from under + hand. Sense of "secret, stealthy, surreptitious" first recorded 1530s. For sense development, cf. Middle Dutch onderhanden "by degrees, slowly," Dutch onderhandsch "secret, private." The adjective is attested from 1540s.
underhanded (adj.): in reference to a throw, etc., c.1822, from underhand. As "in secret," from 1825; as "with too few people," from 1834.
underlay (v.): Old English under lecgan "to support by placing something beneath;" see under + lay (v.). Related: Underlaid; underlaying.
underlie (v.): Old English under licgan "to be subordinate to, to submit to;" see under + lie (v.2). Meaning "to lie under or beneath" is attested from c.1600; figurative sense of "to be the basis of" is attested from 1852 (implied in underlying).
underline (v.): 1721, from under + line (v.). Cf. Dutch onderlijnen. Related: Underlined; underlining. The noun is attested from 1888.
underling (n.): late 12c., from under + diminutive suffix -ling.
undermine (v.): c.1300, undermyne, from under + mine (v.). The figurative sense is attested from early 15c. Cf. Dutch ondermijnen, Danish underminere, German unterminiren. Related: Undermined; undermining.
underneath (adv.): Old English underneoðan, from under + neoðan "below" (see beneath).
undernourished (adj.): also under-nourished, 1910, from under + past participle of nourish.
underpants (n.): 1931, from under + pants. Drove out drawers, knickers in this sense.
underpass (n.): 1904, American English, from under + pass (n.).
underpin (v.): 1520s (figurative); 1530s (literal), from under + pin (v.). Related: Underpinned; underpinning.
underpinning (n.): late 15c., "action of supporting or strengthening from beneath," from under + present participle of pin (v.). Figurative sense of "prop, support" is recorded from 1580s.
underprivileged (adj.): 1896, from under + past participle of privilege (v.). Noun use is attested from 1935.
underrate (v.): also under-rate, 1640s, "to esteem at too little worth," from under + rate (v.). Related: Underrated; underrating.
underscore (v.): 1771, "to draw a line under," from under + score (v.). The figurative sense of "to emphasize" is attested from 1891. Noun meaning "a line drawn below (something)" is recorded from 1901.
undersea: 1610s, from under + sea.
underserve (v.): "to serve insufficiently," 1710, from under + serve (v.). Related: Underserved; underserving.
undershirt (n.): 1640s, from under (adj.) + shirt (n.). Cf. North Frisian onnersjürt, Danish underskjorte.
undershoot (v.): 1660s, "to shoot too low," from under + shoot (v.). In reference to aircraft or pilots, recorded from 1918. Undershot as a type of water wheel is recorded from c.1600.
underside (n.): c.1680, from under + side (n.). Cf. Dutch onderzijde, Danish underside, German unterseite.
undersign (v.): 1570s, from under + sign (v.). Related: Undersigned; undersigning.
understand (v.): Old English understandan "comprehend, grasp the idea of," probably literally "stand in the midst of," from under + standan "to stand" (see stand). If this is the meaning, the under is not the usual word meaning "beneath," but from Old English under, from PIE *nter- "between, among" (cf. Sanskrit antar "among, between," Latin inter "between, among," Greek entera "intestines;" see inter-).

That is the suggestion in Barnhart, but other sources regard the "among, between, before, in the presence of" sense of Old English prefix and preposition under as other meanings of the same word. "Among" seems to be the sense in many Old English compounds that resemble understand, e.g. underniman "to receive," undersecan "to investigate," underginnan "to begin." It also seems to be the sense still in expressions such as under such circumstances.

Perhaps the ultimate sense is "be close to," cf. Greek epistamai "I know how, I know," literally "I stand upon." Similar formations are found in Old Frisian (understonda), Middle Danish (understande), while other Germanic languages use compounds meaning "stand before" (cf. German verstehen, represented in Old English by forstanden). For this concept, most Indo-European languages use figurative extensions of compounds that literally mean "put together," or "separate," or "take, grasp" (see comprehend). Old English oferstandan, Middle English overstonden, literally "over-stand" seem to have been used only in literal senses.
understandable (adj.): late 14c., "able to understand;" late 15c., "able to be understood," from understand + -able. Related: Understandably.
understanding (n.): Old English understandincge "comprehension," from understand (q.v.). Meaning "mutual agreement" is attested from 1803.