Abstract: The mirror instability and electromagnetic ion cyclotron (EMIC) instability, driven by ion perpendicular temperature anisotropy, are ubiquitous in space plasmas and play important roles on the evolution of substorm and storm.This paper outlines the physical mechanisms of these two instabilities based on magnetohydrodynamics (MHD) and kinetic theory, and reviews the fundamental theoretical research results on the two instabilities under the condition of a single ion component (proton). The progress on two types of instability in multi-component ions was further reviewed with a focus on exploring the impact of the heavy ions (He⁺、O⁺) in the Earth's magnetosphere on these two types of instability. The theoretical derivation and numerical simulation related to instability thresholds and growth rates in multi-ion plasmas were summarized, and challenges in current research were dynamically analyzed including but not limited to non-Maxwellian ion distributions and nonlinear evolution of instability. To comprehensively reveal the regulatory effects of multi-ion components on these two types of instability and their significance in global kinetics, future research requires a combination of more systematic theories, advanced numerical simulations, and more satellite observations, which will provide important basis for a deeper understanding of energy transport and wave particle interactions in space plasmas.