They are the second major-professional ice hockey team to represent the city of Kyiv, preceded only by its short lived predecessor, also named Dynamo (founded in 1953).

Sokil is accredited with developing a majority of the country's top young hockey players, producing NHL All Stars such as Dmytro Khrystych and Oleksiy Zhytnyk, and Stanley Cup Champions Ruslan Fedotenko and Anton Babchuk.

Though the team would finish 6th in its inaugural season, they would go on to have the best record in their division the following year; earning a promotion to the top level of competition in the Soviet leagues.

The final three years under the Dynamo name would show gradual, albeit slow improvements; each season finishing one place higher in the standings.

The historical white and blue colors of the Dynamo sports society would be kept intact, but the team would adopt the name of the "Falcon", or "Sokil" in Ukrainian.

In their first season back, great goaltending by Konstantin Gavrilov managed to overcome a poor offense, and ultimately allowed the team squeak into the playoffs, bypassing Avtomobilist Sverdlovsk by a mere point.

Sokil would remain competitive, but the addition of homegrown forward Dmytro Khrystych and defenseman Oleksandr Hodyniuk in 1985 and 1986, respectively, would elevate the team to new heights.

Bogdanov's dismissal did little to curtail the franchise's downward spiral, with the team reaching new record lows with head coach Alexander Fedeev at the helm.

Future Olympian and Stanley Cup champion, Ruslan Fedotenko would leave the team in 1996 to pursue his NHL dreams.

Kyivans Anton Babchuk and Nikolai Zherdev, products of the Sokil junior development program, would later be recruited by Elektrostal scouts in the Russian Major League.

With the dissolution of the IHL, orphaned teams from the Soviet Bloc found a home in the newly formed Eastern European Hockey League.

Benefiting from a lower level of competition than that of the Russian league, and new head coach Oleksandr Seukand, the team would find renewed success.

Sokil players like Valentyn Oletsky (1997, 2000) and Dmitri Markovskiy (1998) would secure scoring titles, Konstantin Kasyanchuk was awarded league forward MVP in 2001, and Vadim Seliverstov was named top goaltender in 2003.

In spite of government cuts to hockey programs in the city, the team would realign its franchise with Russia, though this time with the more modest Russian Major League.

The newly revived team was met with continued success in the Russian league, finishing with the best regular season record that year; 4th overall in points percentage.

They would qualify for a bye in the first round, handily defeat Ryazan in the secondaries, but would ultimately fall to Yugra Khanty-Mansiysk in a 3–1 lopsided series.

They would face further financial difficulties, losing players along the way (including Varlamov), and finish 4th in the Belarusian league's standings, ultimately falling to Yunost Minsk in the semifinals.

This element has remained constant on both the chest piece as well as the shoulder patches throughout the team's history since adopting the "Sokil" name.

The re-branding saw a modernization of the team's crest; with a new and more aggressive falcon centerpiece, while retaining the classic, albeit broadened, chestnut leaf backdrop.

The most notable players drafted from Sokil are defenseman Alexei Zhitnik, who played more the 1000 regular season games in the NHL, and forward Dmitri Khristich, who scored over 250 goals and 500 points.