Over the last decades it has become routine to form beams of positrons and antiprotons and to use them to produce trapped samples of both species for a variety of purposes. Positrons can be captured efficiently, for instance using a buffer-gas system, and in such quantities to form dense, single component plasmas useful for antihydrogen formation. The latter is possible using developments of techniques for dynamically capturing and then cooling antiprotons ejected from the Antiproton Decelerator at CERN. The antiprotons can then be manipulated by cloud compression and evaporative cooling to form tailored plasmas. We will review recent advances that have allowed antihydrogen atoms to be confined for the first time in a shallow magnetic minimum neutral atom trap superimposed upon the region in which the antiparticles are held and mixed. A new mixing technique has been developed to help achieve this using autoresonant excitation of the centreofmass longitudinal motion of an antiproton cloud. This allows efficient antihydrogen formation without imparting excess energy to the antiprotons and helps enhance the probability of trapping the anti-atom.