Quantum spin liquids (QSLs) represent a novel state of matter in which quantum fl uctuations prevent the conventional magnetic order from being established, and the spins remain disordered even at zero temperature. There have been many theoretical developments proposing various QSL states. On the other hand, experimental movement was relatively slow largely due to limitations on the candidate materials and difficulties in the measurements. In recent years, the experimental progress has been accelerated. In this topical review, we give a brief summary of experiments on the QSL candidates under magnetic fields. We arrange our discussions by two categories: i) Geometrically-frustrated systems, including triangular-lattice compounds YbMgGaO4 and YbZnGaO4,κ-(BEDT-TTF)2Cu2(CN)3, and EtMe3Sb[Pd(dmit)2]2, and the kagomésystem ZnCu3(OH)6Cl2;ii) the Kitaev materialα-RuCl3. Among these, we will pay special attention toα-RuCl3, which has been intensively studied by ours and other groups recently. We will present evidence that both supports and rejects the QSL ground state for these materials, based on which we give several perspectives to stimulate further research activities.