We establish the low-temperature phase diagrams of the spin-1/2 and spin-1 Kondo lattice models as a function of the conduction-band filling n and the exchange coupling strength J in the regime of ferromagnetic effective exchange interactions (n 0.5). We show that both models have several distinct ferromagnetic phases separated by continuous Lifshitz transitions of the Fermi-pocket vanishing or emergence type: one of the phases has a true gap in the minority band (half metal), the others only a pseudogap. They can be experimentally distinguished by their magnetization curves; only the gapped phase exhibits magnetization rigidity. We find that, quite generically, ferromagnetism and Kondo screening coexist rather than compete, both in spin-1/2 and spin-1 models. We compute the Curie temperatures and establish a "ferromagnetic Doniach diagram" for both models. PACS numbers: 71.27.+a, 72.15.Qm, 75.20.Hr, 75.30.Kz, 75.30.Mb Materials with competing interactions, such as many lanthanide and actinide compounds, have complex lowtemperature phase diagrams with different ground states [1][2][3][4][5][6]. The Kondo lattice model (KLM) [7-9] describes a conduction band of itinerant electrons and a lattice of local moments on f shells, coupled at each site by an antiferromagnetic exchange interaction J. For large J, the moments are screened. The resulting paramagnetic state has Fermi liquid properties with strongly renormalized parameters. For small J, the conduction-band electrons are carriers of longrange magnetic interactions and the moments order. The two regimes are separated by a quantum phase transition at critical J * , as described by the Doniach diagram [10]. The Néel temperature increases at first quadratically with J, but then it peaks and decreases to zero at J * as the Kondo screening takes over. The simplest version of the KLM with spin-1/2 moments indeed has an antiferromagnetic (AFM) ground state (Néel order) for small J near half-filling [11,12]. The nature of the phase transition at J * has been investigated using a variety of methods, the most accurate of which confirm that the transition is second order (quantum critical) and indicate that it involves a change of the Fermi surface topology [13][14][15]. In the spin-1 KLM, there is no phase transition at half-filling and the AFM phase extends to large values of J. While most cerium compounds show AFM order, some are ferromagnetic (FM): CeRu 2 Ge 2 [16], CeIn 2 [17, 18], and CeRu 2 Al 2 B [19]. A number of uranium and neptunium heavy-fermion materials are also FM: UTe [20], UCu 0.9 Sb 2 [21], UCo 0.5 Sb 2 [22], NpNiSi 2 [23], Np 2 PdGa 3 [24], and UCu 2 Si 2 [25]. In addition, there are strong indications of robust coexistence of the Kondo effect and ferromagnetism, in particular in U compounds. In Refs. [25 -29] it has been proposed that an appropriate minimal model for this behavior is the spin-1 version of the KLM, where in the mean-field picture the conduction-band electrons underscreen the local moments, while the residual moments order ferromagnet...