Real rank was introduced by Brown and Pedersen in 1991 as a variant of stable rank, generalizing a characterization of covering dimension in terms of the instability of tuples of continuous functions. Nuclear dimension, introduced by Winter and Zacharias in 2010, generalizes a different characterization of covering dimension, based on the colorability of refinements of open covers. The two notions agree for commutative C*-algebras, where they coincide with the covering dimension of the spectrum, but differ already for homogeneous C*-algebras. In this talk, I will recall both notions of dimension, discuss examples illustrating their differences, and sketch the proof of the main result: the real rank of a C*-algebra is bounded above by its nuclear dimension.