In the Prologue, we meet Tevye the milkman and his wife Golde, and the people of Anatevka, a small Jewish settlement in Russia.  It is 1905 and the first rumblings of the Russian Revolution are to be heard.

Life in Anatevka is hard, and governed by the traditions of the Jewish way of life, with marriages arranged by the village matchmaker Yente.  She has been to see Golde, to arrange a marriage for Tzeitel, the oldest daughter, with the rich but elderly Lazar Wolf, the village butcher.  Tzeitel, Hodel and Chava, the three sisters sing of the matches they would like to be arranged for their perfect husbands.

Tevye then enters, pulling his cart, and muses "If I was a rich man", but his dreams are interrupted by various people, and the news that Jews from adjacent villages are being evicted.  Enter Perchick, a student from Kiev University, wandering, but earning a living from giving lessons to children; Tevye invites him to spend the Sabbath with them, and he is soon involved with Hodel, Tevye's second daughter.  After some confusion, Tevye and Lazar Wolf agree to Tzeitel's betrothal, but when Tevye tells Tzeitel the good news she is overcome and has to reveal that all along, she has loved Motel the tailor.  She is so upset that Tevye agrees (after persuasion) that she may marry him and not Lazar Wolf; this then has to be explained to Golde.

This is cleverly done by the appearance, in a dream, of Lazar's deceased first wife, Fruma-Sarah, who tells off dire consequences of Lazar remarrying.  Golde agrees to the marriage pf Tzeitel and Motel.  The marriage is celebrated, but after a joyous dance, the Constable enters with his men and breaks up the ceremony as a prelude to a pogrom. Act Two opens with Perchick on his way back to Kiev to tack part in the revolution but, before he goes he asks Hodel to marry him.  They tell Tevye that they will marry in defiance of the tradition that they should ask him, and despite his opposition, he agrees.  He bravely tells Golde of his decision and why he did it - because Hodel loves Perchick - and asks if she loves him and this leads to the loveliest duet in the show - "Do you love me?"

Then rumours start about Hodel and Perchick (who has been arrested in Kiev) followed by a new arrival in Motel's shop, where Chava, the third daughter has once again be approached by Fyedka, a Russian.  Fyedka has been interested in Chava for some time but she has held off due to Tevye's traditional Jewish hatred of all things Russian would never allow him to accept Fyedka as his son-in-law.  Now she realises that she loves him, and tries to ask Tevye to accept Fyedka but he cannot and tells her never to see him again.  She decides instead to run away with him.

On top of this disaster, the Constable warns Tevye that the whole village has but three days to clear out - the pogrom - has started - there is talk of resistance but it is hopeless: and Anatevka has to be abandoned. 

The opera ends with the villagers, one after the other going away to start a new life wherever the may, leaving Tevye, Golde, and their youngest two daughters, Shprintze and Bielke packed and ready to go to America, leaving Anatevka empty, deserted, silent.