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The high surface charge carrier densities, accumulated by the electrostatic gating of two-dimensional (2D) materials with ionic liquids (ILs), have often been exploited in 2D transistors and devices. However, the intrinsic liquid nature, sensitivity to humidity, and the stress induced in frozen liquids prevent them from forming an ideal platform for electrostatic gating and surface probe techniques. This dissertation reports a lithium-ion (Li-ion) solid electrolyte substrate (or simply Li-ion glass) alternative to ILs, by demonstrating its application in high-performance transistors and circuits using 2D transition metal dichalcogenide (TMD). The back-gated n-type MoS² and p-type WSe² transistors resulted in sub-threshold values approaching the ideal limit of 60 mV/dec while maintaining a high ON/OFF ratio (> 10⁶) and a complementary inverter amplifier gain of 34 under a 1 V supply, the highest among comparable solid-state amplifiers. Microscopic studies using microwave impedance microscopy clearly show a uniform and homogeneous channel formation, indicating a smooth interface between the TMD and the underlying electrolytic substrate. This dissertation also reports the direct growth of few-layer (3-4L) single-crystal MoS² on lithium-ion solid electrolyte substrate by chemical vapor deposition (CVD) and demonstrates efficient gate control in the as-grown crystal via electrolytic gating. The gating efficiency of the transistors fabricated on the as-grown crystals, and back-gated by the solid electrolyte, are comparable to the devices with exfoliated and transferred material with an additional gain in mobility value. Field-effect mobility in the range of 42-49 …