Methods for purifying RNA from a sample, comprising one or more steps of tangential flow filtration, hydroxyapatite chromatography, core bead flow-through chromatography, or any combinations thereof. These techniques are useful individually, but show very high efficiency when used in combination, or when performed in particular orders. The methods can purify RNA in a highly efficient manner without unduly compromising potency or stability, to provide compositions in which RNA is substantially cleared of contaminants. Moreover, they can be performed without the need for organic solvents.