Medievalism is a term to describe concepts, practices, or thoughts which originated in the Middle Ages on the planet Earth. The Middle Ages consisted of a time period ranging from approximately 8th century to the 17th century. These terms also apply to the equivalent period of an alien culture's development as well.
Leonard McCoy, upon observing 20th century medical practices, in particular the treatments of chemotherapy and fundoscopic examination, stated that he was "dealing with medievalism." (Star Trek IV: The Voyage Home)
In a discussion between Tom Paris and The Doctor, Paris described the exhilaration of cruising up Highway 1 through Northern California in a fully stock 1969 Chevy Camaro, where "the woofers are pounding, the wind is whipping through your hair." The Doctor added to Paris' fantasy, the fact that the car possessed "medieval safety constraints, internal combustion system producing lethal levels of carbon monoxide." (VOY: "Vis à Vis")
In 2153, Tarquin gave Hoshi Sato a book written in a language that had been dead for over a thousand years old. Upon translating it, Hoshi noted that "it's an interesting language, reminds me of medieval Klingon. (ENT: "Exile")
During a confrontation between John Frederick Paxton and Charles Tucker, in early 2155, Paxton compared Tucker's relationship with T'Pol to be like the one between Romeo and Juliet, "the two star-crossed lovers," stating, "I can't help but wonder whether your little drama will end happier than that famous double suicide in a medieval tomb." (ENT: "Demons")
While facing the reality that Spock might die under his care, in 2270, the frustrated Dr. McCoy stated that "what's the use of being a doctor, anyway? We're only as good as our drugs and technology make us. Underneath all the tricks, I might as well be practicing in the Middle Ages." As a show of his support, Kirk chimed in, stating, "If you really believed that, Bones, you wouldn't still be a doctor after 25 years. (TAS: "The Pirates of Orion")
Prior to a racquetball game between Miles O'Brien and Julian Bashir, in 2370, Keiko O'Brien gave her husband a silk handkerchief that was decorated with a medieval Japanese design scented with her perfume as a token of good luck. (DS9: "Rivals")
While researching various species concepts on suicide, in 2372, Kathryn Janeway discussed with Tuvok the "double effect" principle on assisted suicide, a concept that relates to the relief of suffering, which dated back to the Bolian Middle Ages. (VOY: "Death Wish")