In this talk, I will present a series of recent works, in part joint with H. Kwon, V. Giri, and V. Vicol. The common theme throughout is that the weak solutions we construct are intermittent; that is, they display deviations from the scaling laws predicted by Kolmogorov’s 1941 theory of turbulence. The techniques we have developed allow us to (1) prove a ”strong” version of Onsager’s famous conjecture, and (2) construct solutions to 3D Euler with well-defined helicity which is not conserved.