[Popper's epistemology] is worked out on such a scale, and yet in such detail, that it constitutes an intellectual achievement of the front rank. It is the most highly developed philosophy yet to have appeared that incorporates within itself a belief in an independently existing material world subsisting in independently existing space and time. It constitutes a huge advance beyond Russell, and embodies a depth of originality and imagination altogether outside Russell's scope. Anyone who is determined to cling to the empiricist tradition will find in Popper's philosophy the richest and most powerful instantiation of it that the ongoing development of Western philosophy has made available to us so far. At the point we have reached around the year 2000, to be a self-aware and sophisticated empiricist has to mean either being a Popperian or being a critical and reconstructed Popperian. And to be any sort of transcendental idealist ought to involve embracing something like a Popperian account of empirical reality. On either presupposition, he is the foremost philosopher of the age.
Confessions of a Philosopher, by Bryan Magee, pg 193:
Many a times when i listened to natural scientists talking about what they do they describe Poppers Views without naming him. Some don't even seem to know Popper at all. If that doesn't show his importance i don't know.