Online Etymology Dictionary

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 (adj.): 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.). Similar formation in North Frisian onnersjürt, Danish underskjorte. Old English had undersyrc (see sark (n.)).
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.): 1680s, from under (adj.) + side (n.). Similar formation in 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 (v.)). If this is the meaning, the under is not the usual word meaning "beneath," but from Old English under, from PIE *nter- "between, among" (cognates: Sanskrit antar "among, between," Latin inter "between, among," Greek entera "intestines;" see inter-). Related: Understood; understanding.

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, such as underniman "to receive," undersecan "examine, investigate, scrutinize" (literally "underseek"), underðencan "consider, change one's mind," 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;" compare 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" (German verstehen, represented in Old English by forstanden "understand," also "oppose, withstand"). 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. For "to stand under" in a physical sense, Old English had undergestandan.
understandable (adj.): late 14c., "able to understand;" late 15c., "able to be understood," from understand + -able. Related: Understandably.
understanding (n.): Old English understanding "comprehension," verbal noun from understand (v.). Meaning "mutual agreement" is attested from 1803.
understate (v.): 1781, from under + state (v.). Related: Understated; understating.
understated (adj.): 1939, of clothing, fashions, writing, etc., figurative use of the past participle of understate (v.).
understatement (n.): 1799, from under + statement.
understory (n.): in reference to forest vegetation, also under-story, 1902, from under + story (n.).
understudy (v.): also under-study, 1852, in the theatrical sense "memorize a part so as to be capable of performing on short notice it in the absence of the one to which it is assigned," from under + study (v.). The noun is attested from 1848, translating Italian supplimento.
undertake (v.): c. 1200, "to entrap;" c. 1300, "to set about (to do)," from under + take (v.). Similar formation in French entreprendre "to undertake," from entre "between, among" + prendre "to take." The under in this word may be the same one that also may form the first element of understand. Old English had underniman "to trap, accept" (cognate with Dutch ondernemen, German unternehmen).
undertaker (n.): c. 1400, "a contractor or projecter of any sort," agent noun from undertake (v.). The specialized sense (1690s) emerged from funeral-undertaker.
undertaking (n.): "enterprise," early 15c., verbal noun from undertake (v.). An Old English word for this was underfangenes.
undertone (n.): 1762, "low or subdued tone," from under + tone (n.). Figurative sense of "undercurrent of feelings, etc.," is attested from 1861.
undertow (n.): 1798, from under + tow (n.).
underutilize (v.): also under-utilize, 1949, from under + utilize. Related: Underutilized; underutilizing.
undervalue (v.): 1590s, "to rate as inferior in value" (to), from under + value (v.). Sense of "to estimate or esteem too low" is recorded from 1610s. Meaning "to rate at too low a monetary value" is attested from 1620s. Related: Undervalued; undervaluing.
underwater (adj.): 1620s, from under + water (n.1). Of mortgages from 2008.
underway (adv.): 1749, of ships, "having begun to move," from under + way (n.). In reference to projects, activities, etc., it is attested from 1935.
underwear (n.): "undergarments," 1872, from under + wear (n.). So called because they are worn under one's clothing.
underweight (adj.): 1899, from under- + weight.
underwhelm (v.): 1953 (implied in underwhelming), a facetious play on overwhelm, with under. Related: Underwhelmed; underwhelmingly.
underworld (n.): c. 1600, "the lower world, Hades, place of departed souls," also "the earth, the world below the skies," as distinguished from heaven. Similar formation in German unterwelt, Dutch onderwereld, Danish underverden. Meaning "lower level of society" is first recorded 1890; "criminals and organized crime collectively" is attested from 1900.
underwrite (v.): Old English underwritan "write at the foot of; subscribe;" see under + write (v.). A loan-translation of Latin subscribere (see subscribe). Used literally at first; modern sense of "to accept the risk of insurance" (1620s) is from notion of signing a marine insurance policy. Meaning "to support by a guarantee of money" is recorded from 1890.
underwriter (n.): 1610s, "subscriber," agent noun from underwrite (v.). Insurance sense is from 1620s.
undeserved (adj.): late 14c., from un- (1) "not" + past participle of deserve (v.). Related: Undeservedly.
undeserving (adj.): 1540s, from un- (1) "not" + present participle of deserve (v.).
undesirable (adj.): 1660s, "not to be desired, objectionable," from un- (1) "not" + desirable. The noun meaning "undesirable person or thing" is first attested 1883. Undesired "not asked or invited" is recorded from late 15c.
undetectable (adj.): 1789, from un- (1) "not" + detectable (see detect (v.)).
undetected (adj.): 1590s, from un- (1) "not" + past participle of detect (v.).
undetermined (adj.): mid-15c., from un- (1) "not" + past participle of determine (v.).
undeterred (adj.): c. 1600, from un- (1) "not" + past participle of deter (v.).
undeveloped (adj.): 1736, from un- (1) "not" + past participle of develop (v.). In reference to film, it is attested from 1939.
undeviating (adj.): 1732, from un- (1) "not" + present participle of deviate.
undeviating (adj.): 1732, from un- (1) "not" + present participle of deviate (v.).
undies (n.): 1906, diminutive euphemistic abbreviation for women's underwear (or undergarments).
undifferentiated (adj.): 1862, from un- (1) "not" + past participle of differentiate (v.).
undigested (adj.): 1520s, from un- (1) "not" + past participle of digest (v.). Figurative sense is recorded from c. 1600.
undignified (adj.): 1680s, of clergy, "not holding a position of dignity," from un- (1) "not" + dignified. Meaning "lacking in dignity of manner" is attested from 1782.
undiluted (adj.): 1756, from un- (1) "not" + past participle of dilute (v.).
undiminished (adj.): 1580s, from un- (1) "not" + past participle of diminish (v.).
undine (n.): female water spirit, 1821, from Modern Latin Undina (1650s), coined by Paracelsus ("De Nymphis") in his alchemical system, from Latin unda "a wave, billow" (see water (n.1)). Popularized by German romance "Undine, eine Erzählung" (1811) by Baron F.H.C. La Motte Fouqué. Undinism (1928) was coined by sex researcher Havelock Ellis to describe the fetish for urine (which Ellis had); nowadays it would be called urophilia.
undisciplined (adj.): late 14c., "untrained," from un- (1) "not" + past participle of discipline (v.). Similar formation in German undisciplinirt, Swedish odisciplinerad. Specific meaning "not subject to military discipline" is attested from 1718.
undisclosed (adj.): 1560s, from un- (1) "not" + past participle of disclose (v.).