In major scales, the mediant chord is a minor triad and is symbolized with the Roman numeral iii.
In natural minor scales, the mediant is a major triad and is symbolized with the Roman numeral III.
Tonicization or modulation to the mediant is quite common in pieces written in the minor mode and usually serves as the second theme group in sonata form since it is very easy to tonicize III in minor.
It becomes more common in late Haydn and Mozart and normal by middle-period Beethoven.
Mediant tonicization in major is an important feature of Romantic music.