The ATRAP experiment at the CERN antiproton decelerator AD aims for a test of the CPT invariance by a high precision comparison of the 1s-2s transition in the hydrogen and the antihydrogen atom. Antihydrogen production is routinely operated at ATRAP and detailed studies have been performed in order to optimize the production efficiency of useful antihydrogen. The shape parameters of the antiproton and positron clouds, the n-state distribution of the produced Rydberg antihydrogen atoms and the antihydrogen velocity have been studied. Furthermore an alternative method of laser controlled antihydrogen production was successfully applied. For high precision measurements of atomic transitions cold antihydrogen in the ground state is required which must be trapped due to the low number of available antihydrogen atoms compared to the cold hydrogen beam used for hydrogen spectroscopy. To ensure a reasonable antihydrogen trapping efficiency a magnetic trap has to be superposed the nested Penning trap. First trapping tests of charged particles within a combined magnetic/Penning trap have started at ATRAP.