In connection to the theory of hydrodynamic turbulence, Onsager conjectured that solutions to the incompressible Euler equations with Holder regularity below 1/3 may dissipate energy. Recently, DeLellis and Székelyhidi have adapted the method of convex integration to construct energy-dissipating solutions with regularity up to 1/10. In a two lecture series, we will discuss Onsager’s conjecture, its relation to turbulence, and how one can use convex integration to construct solutions with regularity up to 1/5 which have compact support in time.