The oceans cover 70% of the planet's surface, and their planktonic inhabitants generate about half the global primary production, thereby playing a key role in modulating planetary climate via the carbon cycle. The ocean biota have been under scientific scrutiny for well over a century, and yet our understanding of the processes driving natural selection in the pelagic environment - the open water inhabited by drifting plankton and free-swimming nekton - is still quite vague. Because of the fundamental differences in the physical environment, pelagic ecosystems function differently from the familiar terrestrial ecosystems of which we are a part. Natural selection creates biodiversity but understanding how this quality control of random mutations operates in the oceans - which traits are selected for under what circumstances and by which environmental factors, whether bottom-up or top-down - is currently a major challenge. Rapid advances in genomics are providing information, particularly in the prokaryotic realm, pertaining not only to the biodiversity inventory but also functional groups. This essay is dedicated to the poorly understood tribes of planktonic protists (unicellular eukaryotes) that feed the ocean's animals and continue to run the elemental cycles of our planet. It is an attempt at developing a conceptually coherent framework to understand the course of evolution by natural selection in the plankton and contrast it with the better-known terrestrial realm. I argue that organism interactions, in particular co-evolution between predators and prey (the arms race), play a central role in driving evolution in the pelagic realm. Understanding the evolutionary forces shaping ocean biota is a prerequisite for harnessing plankton for human purposes and also for protecting the oceanic ecosystems currently under severe stress from anthropogenic pressures.