In this talk, I will discuss some general properties of effective theories of Goldstone bosons in which Lorentz symmetry is spontaneously broken. I will first introduce an extension of Goldstone theorem to systems with a finite density of charge. This very general setting is potentially applicable to contexts as diverse as early universe cosmology and QCD at finite density. Additionally, I will show how certain effective theories of Goldstones with broken Lorentz symmetry admit UV completions that do not restore any broken symmetry.