A central object of interest in the study of gauge theory are Yang--Mills connections. Special classes of solutions exist on many classes of manifolds: flat connections, ASD instantons on 4-manifolds, Hermitian Yang--Mills connections on Kaehler manifolds, etc. The purpose of this minischool is to familiarize the participants with $\mathrm{G}_2$-instantons (which are certain Yang-Mills connections on $\mathrm{G}_2$-manifolds). I will discuss the basic properties of $\mathrm{G}_2$-instantons, discuss their deformation theory, and explain one construction method (based on joint work with Henrique Sa Earp). Time permitting, I will discuss some points of the known compactness results regarding $\mathrm{G}_2$-instantons (due to Uhlenbeck, Price, Nakajima, Tian).