Thermally activated magnetization reversal is of great importance in areas such as permanent magnetism and magnetic recording. In spite of many decades of scientific research, the phenomenon of slow magnetization dynamics has remained partially controversial. It is now well-established that the main mechanism is thermally activated magnetization reversal, as contrasted to eddy currents and structural aging, but the identification of the involved energy barriers remains a challenge for many systems. Thermally activated slow magnetization processes proceed over energy barriers whose structure is determined by the micromagnetic free energy. This restricts the range of physically meaningful energy barriers. An analysis of the underlying micromagnetic free energy yields power-law dependences with exponents of 3/2 or 2 for physically reasonable models, in contrast to arbitrary exponents m and to 1/H-type laws.