We review recent work on the instability of the heavy Fermi liquid state (FL) of the Kondo lattice towards a magnetic metal in which the local moments are not part of the Fermi sea. Using insights drawn from the theory of deconfined quantum criticality of insulating antiferromagnets, we discuss the possibility of a direct second-order transition between the heavy Fermi liquid and such a magnetic metal. We suggest the presence of at least two distinct diverging time scales - the shorter one describes fluctuations associated with the reconstruction of the Fermi surface, while a longer one describes fluctuations of the magnetic order parameter. The intermediate time scale physics on the magnetic side is suggested to be that of a novel fractionalized Fermi liquid (FL*) state with deconfined neutral S=12 excitations. This could ultimately devolve into the magnetic phase with conventional order at one of the larger time scales. Experimental implications for this scenario are noted.