Here, I use the phrase ‘intelligent universe’ to refer to all intelligent entities everywhere. Whether the set of all such entities overlaps with, or is a subset of, the biological universe depends on whether we include artificial intelligence in it. I focus here on biological intelligence. On Earth, evolution to high intelligence has proceeded via a series of milestones. These include: multicellularity, bilaterality, brain, and dexterity. To what extent does evolution towards high intelligence elsewhere proceed via the same milestones? I suggest that similar steps would often be found to characterize evolution on other inhabited planets, providing it can continue for long enough. I put forward the hypothesis that there are at least a trillion radio-level intelligences in the observable universe right now. Then I consider the possible implications of ‘first contact’ between humans and one of them. Such contact could pose a threat for human survival. Finally, I look at home-grown threats, including the fixed mind-sets that underlie religious fundamentalism and science denial. I end by urging a robust defence of both science and humanity against such unthinking views.