We demonstrate coherent microwave control of the rotational, hyperfine, and Zeeman states of ultracold CaF molecules, and the magnetic trapping of these molecules in a single, selectable quantum state. We trap about 5 × 10 3 molecules for almost 2 s at a temperature of 70ð8Þ μK and a density of 1.2 × 10 5 cm −3 . We measure the state-specific loss rate due to collisions with background helium. DOI: 10.1103/PhysRevLett.120.163201 Techniques for producing and controlling ultracold molecules are advancing rapidly, motivated by a wide range of applications. These include precise measurements that test fundamental physics [1,2], quantum state resolved collisions and chemistry [3], quantum computation [4][5][6] and simulation [7,8], and the study of dipolar quantum gases [9]. These applications call for trapped molecules in a single, selectable quantum state, and they typically require coherent control over the rotational and hyperfine states. Such control has recently been achieved [10-13] for bialkali molecules produced by associating ultracold atoms [14][15][16][17][18]. Great efforts are also being made to cool molecules directly, for example, by optoelectrical Sisyphus cooling [19] or direct laser cooling and magneto-optical trapping [20][21][22][23][24][25]. These methods can produce ultracold molecules with greater chemical diversity and with large electric and magnetic dipoles, as is often desired. The magneto-optical trap (MOT) is an excellent tool for collecting and cooling molecules, and it promises to be the starting point for many applications of ultracold molecules, just as it has been for ultracold atoms. However, it does not allow quantum state control, provides limited phase-space density, and has a limited lifetime due to optical pumping into states not addressed by the lasers. Thus, molecules in a MOT must be transferred into a conservative trap where the lifetime can be long, the quantum state can be selected and preserved, and the phase-space density can be increased, for example, by sympathetic, evaporative, or Raman sideband cooling. Magnetic traps have been crucial for exploiting ultracold atoms, and they have previously been used to confine molecules produced at ∼100 mK by buffer-gas cooling and Stark and Zeeman deceleration [26][27][28][29][30][31][32][33]. Here, we demonstrate coherent control and magnetic trapping of laser-cooled molecules, which are key steps towards the applications discussed above. Starting from a MOT of CaF [25], we compress the cloud to increase its density, cool the molecules to sub-Doppler temperature [23], optically pump them into a single internal state, transfer them coherently to a selectable rotational, hyperfine and Zeeman level, and then confine them in a magnetic trap.Our setup is the same as used previously [23,25], with the addition of microwave components to drive the rotational transition. A pulse of CaF emitted at time t ¼ 0 from a cryogenic buffer gas source [34] is decelerated by frequency-chirped counter-propagating laser light [35]. The slowest mo...