For the past four decades, Landau's phenomenological theory of an interacting Fermi system has served as a paradigm for our understanding of metallic behaviour. However, some recent experiments on Ce and U compounds have opened up the possibility of a metallic state which is not a Fermi-liquid. Our objective in this thesis is to try and understand this breakdown of Fermi-liquid theory, and we start with a brief review of Landau's theory in Chap. 2. We begin with the notion of a "quasiparticle" and state how the low-energy transport and thermodynamic response functions depend on the effective mass {dollar}msp*{dollar} of the quasiparticles. We also discuss a slightly different incarnation of the Fermi-liquid that shows up at low temperatures in the Kondo and Anderson models, of magnetic impurities in metals. Here the low-energy excitations can be parametrized with the effective mass as well, which is now related to the inverse of the Kondo temperature {dollar}Tsb{lcub}K{rcub}.{dollar}; In Chap. 3 we present an overview of the experimental scenario, mostly in Ce and U intermetallics which definitely exhibit Kondo-esque logarithmic scattering behaviour at high temperatures. The ground state in these compounds is a paramagnetic metal with a high residual resistivity, but they seem to violate the canonical Fermi-liquid description. We concentrate on two possible mechanisms that can give rise to these anomalous metallic states, namely disorder and Kondo over-screening. The effect of disorder is to create rare regions in the system with a Kondo scale that is essentially zero, thereby destroying the Fermi-liquid. Chap. 4 outlines the methods of solution of correlated impurity and lattice problems; dynamical mean-field theory maps the lattice onto a self-consistently determined Anderson impurity, then Quantum Monte Carlo solves the impurity problem. Using these techniques, the consequences of Kondo disorder in dynamics and magneto-transport are calculated in Chaps. 5 and 6 respectively. Kondo overscreening results from the inability of the conducting host to screen out the magnetic impurity at the largest length scales, or equivalently, the smallest temperatures. Dynamics of an over-screened Kondo lattice is studied in Chap. 7.
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