It has been largely superseded by the term "homosexuality." This also was devised (by a little-known Hungarian doctor, Benkert, who used the pseudonym Kertbeny) in the same year (1869), but at first attracted no attention.

It has, philologically, the awkward disadvantage of being a bastard term compounded of Greek and Latin elements, but its significance--sexual attraction to the same sex--is fairly clear and definite, while it is free from any question-begging association of either favorable or unfavorable character.

(Edward Carpenter has proposed to remedy its bastardly linguistic character by transforming it into "homogenic;" this, however, might mean not only "toward the same sex," but "of the same kind," and in German already possesses actually that meaning.) The term "homosexual" has the further advantage that on account of its classical origin it is easily translatable into many languages.

It is now the most widespread general term for the phenomena we are dealing with, and it has been used by Hirschfeld, now the chief authority in this field, as the title of his encyclopedic work, _Die Homosexualitaet_.
"Sexual Inversion" (in French "inversion sexuelle," and in Italian "inversione sessuale") is the term which has from the first been chiefly used in France and Italy, ever since Charcot and Magnan, in 1882, published their cases of this anomaly in the _Archives de Neurologie_.

It had already been employed in Italy by Tamassia in the _Revista Sperimentale di Freniatria_, in 1878.
I have not discovered when and where the term "sexual inversion" was first used.