Energy deposition of MeV electrons in dense plasmas, critical for fast ignition in inertial confinement fusion (ICF), is modeled analytically. It is shown that classical stopping and scattering dominate electron transport and energy deposition when the electrons reach the dense plasmas in the cores of compressed targets, while "anomalous" stopping associated with self-generated fields and micro instabilities (suggested by previous simulations) might initially play an important role in the lower-density plasmas outside the dense core. We calculate the energy deposition of MeV electrons in precompressed deuterium-tritium (DT) fast-ignition targets, rigorously treating electron energy loss from scattering, longitudinal straggling and transverse blooming. We demonstrate that, while the initial penetration of electrons in a compressed target results in approximately uniform energy deposition, the latter stages involve mutual couplings of energy loss, straggling, and blooming that lead to enhanced, non-uniform energy deposition. These results are critically important for quantitatively assessing ignition requirements for fast ignition.