The self-improving property is a fundamental regularity result in the theory of linear and nonlinear elliptic equations. For nonlocal elliptic equations, however, establishing this property is significantly more complex than in the local setting. We will discuss several key results and arguments that demonstrate this self-improvement of the regularity of the solution. We will also present self-improving properties for equations with fractional Orlicz growth, which is joint work with Kyeong Song (KIAS).