Understanding the cellular mechanisms of drug addiction remains a key task in current brain research. While neuron-based mechanisms have been extensively explored over the past three decades, recent evidence indicates a critical involvement of astrocytes, the main type of non-neuronal cells in the brain. In response to extracellular stimuli, astrocytes modulate the activity of neurons, synaptic transmission, and neural network properties, collectively influencing brain function. G protein-coupled receptors (GPCRs) expressed on astrocyte surfaces respond to neuron- and environment-derived ligands by activating or inhibiting astrocytic signaling, which in turn regulates adjacent neurons and their circuitry. In this review, we focus on the dopamine D1 receptors (D1R) and metabotropic glutamate receptor 5 (mGLUR5 or GRM5)—two GPCRs that have been critically implicated in the acquisition and maintenance of addiction-related behaviors. Positioned as an introductory-level review, this article briefly discusses astrocyte biology, outlines earlier discoveries about the role of astrocytes in substance-use disorders (SUDs), and provides detailed discussion about astrocytic D1Rs and mGLUR5s in regulating synapse and network functions in the nucleus accumbens (NAc)—a brain region that mediates addiction-related emotional and motivational responses. This review serves as a stepping stone for readers of Engineering to explore links between astrocytic GPCRs and drug addiction and other psychiatric disorders.