In the standard cosmological model, galaxies and large-scale structure grew by a process of gravitational instability from initial perturbations which were of the simplest statistical form imaginable: a statistically homogeneous and isotropic Gaussian random field. One of the properties of such a field is that its Fourier transform has real and imaginary parts which are independently Gaussian and consequently the phases are uniformly random. The same thing applies to the phases of the spherical harmonic coefficients involved when observed fluctuations over the celestial sphere, such as in the cosmic microwave background. Defining anything other than random phases as "weird", I discuss various aspects of cosmic weirdness and the non-randomness they produce in harmonic space. I introduce some novel methods for visualizing weirdness in CMB data and elsewhere, and discuss their relationship to more conventional statistical analyses. If I have time I will also discuss a few other interest things to do with CMB fluctuations.