Skyrmions are topologically stable quasiparticles that have been predicted and demonstrated in quantum fields, solid-state physics and magnetic materials, but only recently observed in electromagnetic fields. Here we review the recent advances in optical skyrmions within a unified topological framework. Starting from fundamental theories and classification of skyrmionic states, we describe generation and topological control of different kinds of skyrmions in evanescent, structured and spatiotemporal optical fields. We further highlight generalized classes of optical topological quasiparticles beyond skyrmions and outline the emerging applications, future trends and open challenges. A complex vectorial field structure of optical quasiparticles with versatile topological characteristics emerges as an important feature in modern spin optics, imaging, metrology, optical forces, structured light, and topological and quantum technologies.