Drummer Rami Eskelinen (b. 1967) started to play the drums in a young age, thanks to his musician dad. In 1982 he started his studies at the Pop & Jazz Conservatory of Oulunkylä and played in the summer i.a. in the bands of Tapani Kansa and Meiju Suvas. When Eskelinen graduated in 1988 he was accepted the same year to continue his studies at the jazz department of Sibelius Academy and already on the same year he formed Trio Töykeät with Iiro Rantala and Eerik Siikasaari. This trio developed a unique concept where Rantala's compositions were backed up with the phenomenal musical skills of the trio and their considered arrangements and the repertoire had more humor than the Finnish jazz had on average in the 1980s. Already on it's year of foundation Trio Töykeät won the European jazzgroup contest in Hoeilaart, Belgium. The trio did their first Finnish Jazz Federation tour in 1989 and debut album Päivää! (Sonet) was released the next year.

In 1990-1993 Eskelinen and Rantala studied in New York at the Manhattan School of Music and as the drummer and the pianist returned to Finland Trio Töykeät performed a lot around the world in Cuba, Mexico, Europe, Australia and East Asia. Trio released many high-class albums, and the album released in 1995, Jazzlantis, was awarded with an Emma Award as the Jazz Album of the Year in 1995. In the same year, and the year after that, first Siikasaari and then Rantala were awarded with the Georgie, Yrjö, Award as the Jazzmusician of the Year. Trio Töykeät was also honoured to be the first jazzband ever to play at the Presidential Independence Day Reception in 1996.

In the 21st century the group continued releasing high-class albums and performing actively in Finland and abroad. In 2008 Trio Töykeät however announced that they are, after over 2000 gigs, 43 countries and seven albums, breaking up. There was not any drama involved in the decision to quit: the group just felt that the group has come to the end of their journey. All in all Trio Töykeät was one of the most famous Finnish jazzbands in the 1990's, probably even the most popular.

Besides Trio Töykeät, Eskelinen has played for a long time in Espoo Big Band and taught drums in Ebeli, the pop/jazz department of the music school of Espoo. Eskelinen is a popular musician on the jazz field of Helsinki and he has performed e.g. with Jukka Gustavson Fusion Band and singer/songwriter Laura Sippola's band. Also Piirpauke, the folk/jazzband formed by Sakari Kukko in 1974, has been an important group for Eskelinen since it was re-formed by Kukko in 2010.