Electrically tunable liquid crystal microlenses have attracted strong research attention due to their advantages of tunable focusing, voltage actuation, low power consumption, simple fabrication, compact structure, and good stability. They are expected to be essential optical devices with widespread applications. However, the slow response time of nematic liquid crystal (LC) microlenses has been a significant technical barrier to practical applications and commercialization. LC/polymer composites, consisting of LC and monomer, are an important extension of pure LC systems, which offer more flexibility and much richer functionality than LC alone. Due to the anchoring effect of a polymer network, microlenses, based on LC/polymer composites, have relatively fast response time in comparison with pure nematic LC microlenses. In addition, polymer-stabilized blue phase liquid crystal (PS-BPLC) based on Kerr effect is emerging as a promising candidate for new photonics application. The major attractions of PS-BPLC are submillisecond response time and no need for surface alignment layer. In this paper, we review two types of fast-response microlenses based on LC/polymer composites: polymer dispersed/stabilized nematic LC and polymer-stabilized blue phase LC. Their basic operating principles are introduced and recent progress is reviewed by examples from recent literature. Finally, the major challenges and future perspectives are discussed.