Affine transformations map an equilateral triangle and its incircle resp. circumcircle onto a general triangle and its inscribed ellipse resp. circumscribed ellipse. These ellipses are called Steiner’s inellipse and circumellipse. They are unique with the property that the inellipse is tangent to the sides at their midpoints, and that the circumellipse is centered at the center of gravity of the triangle. After establishing the existence and uniqueness of Steiner’s ellipses, it is shown that these ellipses are related by a homothety with coefficient 2. Steiner’s circumellipse has the smallest area of all circumscribed ellipses, and the Steiner inellipse has the largest area among all inscribed ellipses. Furthermore, Siebeck’s theorem and its connection with Steiner ellipses is proven. If zeros of a cubic polynomial with complex coefficients determine the vertices of a triangle in the complex plane, zeros of the derivative of that polynomial are the foci of Steiner’s inellipse to that triangle. The foci of Steiner’s circumellipse have the property that they are equicevian points of a triangle, which means that these are the points defining three cevians of equal length. This property is proven by analytical and synthetic methods in the last part of the paper.