  High-temperature superconductivity and a wide variety of exotic
superconducting states discovered in FeSe-based materials have been at the
frontier of research on condensed matter physics over the past decade. Unique
properties originating from the multiband electronic structure, strongly
orbital-dependent phenomena, extremely small Fermi energy, electronic
nematicity, and topological aspects give rise to many distinct and fascinating
superconducting states. Here, we provide an overview of our current
understanding of the superconductivity of {\it bulk} FeSe-based materials,
focusing on FeSe and the isovalent substituted FeSe$_{1-x}$S$_{x}$ and
FeSe$_{1-x}$Te$_{x}$. We discuss the highly nontrivial superconducting
properties in FeSe, including extremely anisotropic pairing states, crossover
phenomena from Bardeen--Cooper--Schrieffer (BCS) to Bose--Einstein condensation
(BEC) states, a novel field-induced superconducting phase, and broken
time-reversal symmetry. We also discuss the evolution of the superconducting
gap function with sulfur and tellurium doping, paying particular attention to
the impact of quantum critical nematic fluctuations and the topological
superconductivity. FeSe-based materials provide an excellent playground to
study various exotic superconducting states.
