During the last decade, significant progress has been achieved in the rapidly growing field of the dynamics of hot carriers in metals. Here we present an overview of the recent achievements in the theoretical understanding of electron dynamics in metals, and focus on the theoretical description of the inelastic lifetime of excited hot electrons. We outline theoretical formulations of the hot-electron lifetime that originates in the inelastic scattering of the excited quasiparticle with occupied states below the Fermi level of the solid. First-principles many-body calculations are reviewed. Related work and future directions are also addressed.