  In 1993, just about a century after the epoch of Classical Invariant Theory
and almost 30 years after Mumford's seminal book on Geometric Invariant Theory,
Bernd Sturmfels approached the subject from a new, algorithmic perspective in
his book on Algorithms in Invariant Theory. This article aims to highlight some
of the developments that followed the book. Inspired by Bernd's style of
teaching mathematics, the goal is neither comprehensiveness nor maximal
generality, but to emphasize the main ideas and to convey the beauty of the
subject. The article is intended as an invitation to invariant theory, and in
particular to Bernd's work and the ideas inspired by it.
