Euripides wrote Iphigenia in Taurus before he wrote Iphigenia in Aulis, making Aulis a kind of "prequel" to Taurus. Euripides is one of a trio of great tragedians in fifth-century Greece: Euripides, Sophocles, and Aeschylus. Euripides was renowned during his lifetime, but he was not nearly as popular as either Sophocles or Aeschylus. Sophocles admired Euripides as a master playwright and honored the latter's death by having the participants in the subsequent Dionysian festival dress in mourning rather than in their usual festive costumes.

Philip Vellacott, a twentieth-century translator, explained in Ironic Drama that "as a poet he was revered; in his function as a 'teacher of citizens' he was misunderstood." A century later, Euripides gained more notoriety, if not appreciation. During the fourth century B.C., his plays were more commonly produced and adapted than those of his fifth-century rivals. Aristophanes (448-380 B.C.) dedicated three whole plays to burlesquing—ridiculing—his style. This simple historical fact implies that Athenian audiences must have been familiar enough with Euripides's plays to make Aristophanes's jibes recognizable—Euripides's plays were an institution of drama during this period. While his theater was legendary, it was for his poetry and dramatic artistry for which Euripides was appreciated, not his ideas. Euripides was considered a fine poet with a misguided message. Aristotle (384-322 B.C.) used four of Euripides's works to illustrate various concepts of tragedy in his Poetics, wherein Aristotle defined the standards for drama. In that work he referred to Euripides as "the most tragic of the poets" who nevertheless had many "faults."

Euripides's skepticism was not condoned in the rather conservative fourth century. Greek culture was in decline, and as it declined even further, Euripides's plays were earned to Alexandria, and then to Rome, and the Byzantine culture. Plutarch (c. 46-120 A.D.) related three historical anecdotes of Hellenes who were allowed to escape their enemies by showing proficiency in reciting Euripidean poetry; this evidence corroborates Euripides's reputation, at least as a poet, in ancient Greece.

During the Middle Ages and Renaissance, the very aspect of Euripides's ideas that alarmed his contemporaries, his criticism of the pan-Hellenic gods, fueled an interest in his work by scholars, especially humanists such as Erasmus. Dante mentioned Euripides in his Divine Comedy and Ben Jonson used one of his plays as a model. Euripides's plays (along with those of Aeschylus and Sophocles) were required reading for the classical education valued during the Renaissance. In the seventeenth century Jean Racine adapted many of his plays and considered Euripides his master. John Milton (Paradise Lost) also expressed his admiration.

The eighteenth century lost interest in Euripides because his work was too innovative for the classical revival then in progress. Then Johann Wolfgang von Goethe (Faust) paid him the ultimate Romantic period compliment by calling his work "sublime." Goethe created a new version of Iphigenia in Taurus that follows the original closely. It was of Euripides that Goethe wrote his oft-adapted expression: "Have all the nations of the world since his time produced one dramatist who was worthy to hand him his slippers?"

In the nineteenth century, Robert Browning made conspicuous allusions to certain plays by Euripides, and the Greek playwright was once more instated as a cornerstone of a good, classical education. Gilbert Murray's accessible translations in the early twentieth century made Euripides's work available to the larger public.

Twentieth-century literary criticism holds a reserved judgment regarding Euripides. Modern critics appreciate his championing of the underdog—slaves, women, the elderly, and children— and his lampooning of religious and secular hypocrisy. But he remains a shadowy figure whose actual political and religious beliefs are difficult to discern. Twentieth-century critics are more wary than earlier critics of associating ideas in an artist's works with his personal philosophy. The move toward New Criticism, with its emphasis on the text itself, has had a negative impact on Euripides's reputation in this century.

Under such assessments, Euripides, once again, does not measure up to Sophocles or Aeschylus. Furthermore, twentieth-century readers are accustomed to works of more dramatic intensity than Iphigenia in Taurus, which is considered a "romantic melodrama." Contemporary classical scholars find it interesting for its complex replication and reversal of certain paradigms found in the Oresteia, such as the near sacrifice of a blood relative. It seems unlikely that Iphigenia in Taurus will ever regain the popularity it enjoyed in its day, since its specificity to the status of the Hellenic state in the middle of the Peloponnesian Wars lies at the heart of the play.