Presence of a positive cosmological constant $\Lambda$, however small,
introduces unforeseen conceptual issues in all main areas of gravitational physics. I will first illustrate these in the context of cosmology and black holes, and then focus on gravitational waves. In particular, the celebrated “quadrupole formula” that Einstein derived a century ago was generalized to the positive $\Lambda$ case only last year, and one still does not have an unambiguous, gauge invariant characterization of gravitational waves in full, non-linear general relativity for positive $\Lambda$! The talk will illustrate the richness of opportunities in this area which has received relatively little attention in spite of the strong evidence for accelerated expansion of our universe.