Readily accessible along maintained marked trails and with the exceptional vistas afforded from its summit, it is the hikers' favorite mountain in the western part of the High Tatras.

It reflects the angled appearance of its shape when viewed from the west and south, characterized in the work from 1639 as an "oxtail" (cauda bubula in the Latin original).

[1] The Slovak name is used in other languages including in Polish, rather than its potential Polonized version (Krzywań), except occasionally in Podhale in the immediate vicinity of the Tatras.

[3]The relative elevations of the two mountains were determined by the English natural historian Robert Townson, who ascended both peaks in August 1793 and also made an early recorded comment on Kriváň's aesthetic appeal: The weather was very fine, and the Krivan, having got in the night a cap of snow, looked sublime.

A travel book Ungarisher oder Dacianisher Simplicissimus written by Daniel Georg Speer in 1693 mentions a current legend (may have more ancient roots) explaining how Krivan got its shape.

Although they may not have been the first to do so, it is probable that some of the miners reached the top of Kriváň; remnants of their shacks have survived below Priehyba Ridge at the elevation of about 2,000 m (6,560 ft.) through the present, and the highest, long abandoned, Terézia Shaft is merely about 60 m (200 ft.) below the summit.

[5] The Scottish doctor Townson who ascended it in 1793 provided some evidence that Kriváň was already a recognized occasional destination for tourists in the second half of the 18th century.

His guide from Važec had been to the top several times before and Townson saw him collect small coins from under a summit stone where hikers would leave them for luck.

[6] The first celebrity to attempt ascent of Kriváň was the 30-year-old Habsburg Archduke Joseph in 1806, but the plan was abandoned due to inclement weather although parts of the winding road to the old gold mine high on the slopes had already been improved and a campsite built.

[8] Štúr and a group of locals, Fejérpataky Belopotocký among them, hiked to the top of Kriváň on 16 August, its first recorded ascent that included women.

[14] The mountain is mentioned by Nikolai Gogol as the abode of two Cossack brothers, Ivan and Petro, in his short story 'The Terrible Vengeance', written in 1832.

[15] After lower nobleman Gašpar Fejérpataky Belopotocký (1794–1874) published an account of his 1835 ascent of Kriváň in the literary journal Hronka in 1837, its editor-in-chief Karol Kuzmány (1806–1866) wrote the novella Ladislav (1838), whose title character, taking the long way home from Italy via Germany and the Polish Podhale, hikes to the summit of Kriváň where he and his friends talk about brotherhood among the Slavs, sing arousing songs, and imbibe Tokaj wine.

[21] The role of Kriváň in popular awareness and high culture was highlighted when a country-wide vote in 2005 selected it to be one of the images on Slovakia's euro coins.