There are many examples of interactions between noncommutative algebra and symplectic geometry, the most well-known being the quantization of  (functions on) symplectic manifolds. This talk will discuss other, more recently discovered connections, which touch on the worlds of Lie theoretic representation theory through rational Cherednik algebras, algebraic combinatorics through Macdonald polynomials, integrable systems through the dark art of Dunkl operators, and questions concerning resolutions of singularities in algebraic symplectic geometry.