Lt. Jadzia Dax is the half-humanoid science officer (an attractive 28-year-old trill woman (Lieutenant Jadzia Dax), containing a 300-year old worm).

For those that don't remember, the Trill is a species which forms a symbiotic link with a humanoid life form (Dr. Crusher fell in love with one in "The Host").

Many centuries ago [on the Trills' home world], the symbionts lived underground while the humanoids were on the surface. Due to an environmental disaster, they were forced to join to survive. As time went on this mutual support evolved to become a biological dependency, and thus two individuals became one. They speak with one voice. The symbiont's life span is far longer than the host's and, as a result, one symbiont will be combined with several hosts during its life. When a host dies, doctors surgically remove the symbiont. The worm then burrows itself into the new host.

Dax's host was joined with her when she was an adult. The symbiont part of her is 300 years old, a brilliant scientist with an innate wisdom who can draw upon a library of knowledge built of six lifetimes of experience (Tobin, Dax, Audrid, Torias, Joran, Curzon, and Judzia).

Sisko knew and valued the last person this trill inhabited as one of his most respected teachers (Curzon Dax), and has some deep psychological conflicts with the fact that it now inhabits a beautiful young woman.

Kira forms a very close relationship with Dax and often tells her to loosen up (this sounds like a mixup of whoever's speech this was from; now that the series has started, it seem to be Dax who tells Kira to loosen up). Dax admires Kira for her youthful energy, her purpose and her drive and becomes something of a mentor to her.

Jadzia and Worf roughly started to become romantically invloved since stardate ~50100 (in year 2373) ("Looking for par'Mach in All the Wrong Places"). They went to Risa, pleasure planet, together on stardate ~50280 ("Let He Who is Without Sin").