How are modern samurai related to historical samurai?

It is impossible to follow the old ways of the samurai. Samurai means to serve. You would serve the emperor or the shogun or daiymo, depending when in time you were living. Samurai followed bushido, or way of the warrior, devoting to life and death everything to follow a good path through service. The closet to this in a modern day way would be a Buddhist, serving in the army during the a time of war. Samurai were a class of person in Japan, when the samurai class was disbanded, so was its way of life.