Lithium conducting garnets in the family of Li7La3Zr2O12 (LLZO) are promising lithium conductors for solid-state batteries, due to their high ionic conductivity, thermal stability, and electrochemical stability with metallic lithium. Despite these advantages, LLZO requires a large energy input to synthesize and process. Generally, LLZO is synthesized using solid-state reaction (SSR) from oxide precursors, requiring high reaction temperatures (900-1000 °C) and producing powder with large particle sizes, necessitating high energy milling to improve sinterability. In this dissertation, two classes of advanced synthesis methods – sol-gel polymer-combustion and molten salt synthesis (MSS) – are employed to obtain LLZO submicron powders at lower temperatures. In the first case, nanopowders of LLZO are obtained in a few hours at 700 °C via a novel polymer combustion process, which can be sintered to dense electrolytes possessing ionic conductivity up to 0.67 mS cm-1 at room temperature. However, the limited throughput of this combustion process motivated the use of molten salt synthesis, wherein a salt mixture is used as a high temperature solvent, allowing faster interdiffusion of atomic species than solid-state reactions. A eutectic mixture of LiCl-KCl allows formation of submicrometer undoped, Al-doped, Ga-doped, and Ta-doped LLZO at 900 °C in 4 h, with total ionic conductivities between 0.23-0.46 mS cm-1. By using a highly basic molten salt medium, Ta-doped LLZO (LLZTO) can be obtained at temperatures as low as 550 °C, with an ionic conductivity of 0.61 mS cm-1. The formation temperature can be further reduced by using Ta-doped, La-excess pyrochlore-type lanthanum zirconate (La2Zr2O7, LZO) as a quasi-single-source precursor, which convert to LLZTO as low as 400 °C upon addition of a Li-source. Further, doped pyrochlores can be blended with a Li-source and directly sintered to a relative density up to 94.7% with high conductivity (0.53 mS cm-1). Finally, a propensity for compositional variation in LLZTO powders and sintered ceramics was observed and for the first time explored in detail. By comparing LLZTO obtained from combustion, MSS, and SSR, a correlation between increased elemental inhomogeneity and reduced ionic conductivity is observed. Implications for garnet-based solid-state batteries and strategies to mitigate elemental inhomogeneity are discussed.