Hakusensha was founded by Shueisha in 1973 (which had in turn been founded by Shogakukan decades earlier) and though the three are independent companies, together they form part of the much larger Hitotsubashi Group (with Hakusensha being the youngest and smallest of the three). Because of this partnership, all three's English translations are often published by Viz (which was co-founded by and has a partnership with the Group).
Originally specializing exclusively in shojo manga, only a few months after their founding they launched their flagship manga magazine (Hana to Yume) and within a few years launched some spin-off's which of Hana to Yume which have also come to last for decades including LaLa and Bessatsu Hana to Yume. These have resulted in many major shojo manga franchises and series including Skip Beat!, Patalliro!, Sukeban Deka and Glass no Kamen.
In the 80's, Hakusensha then began to branch out into the other major manga demographics outside of shojo, launching Shonen Jets in 1981 and Silky in 1985. Silky remained ongoing for several decades and was later joined by Melody for the josei demographic but Shonen Jets failed quite quickly and Hakusensha went through several failed manga magazines in the 80's to find a male market, Jets becoming ComiComi, which became Animal House before ultimately resulting in Young Animal (a seinen magazine) which began in 1992.
Since then, Young Animal has shared the distinction with Hana to Yume as being the most frequently published magazines by the publisher (twice a month) and has run a number of very successful manga including Berserk and Futari Ecchi. And though the only Jets magazine ended decades earlier, the Jets Comics brand was used for many Young Animal titles.
Because of Jets' quick end in the early 80's, Hakusensha has virtually no presence in the shonen manga market and continues to focus primarily on shojo and seinen.