The concept of deploying a large number of antennas at the base station, often called massive multiple-input multiple-output (MIMO), has drawn considerable interest because of its potential ability to revolutionize current wireless communication systems. Most literature on massive MIMO systems assumes time division duplexing (TDD), although frequency division duplexing (FDD) dominates current cellular systems. Due to the large number of transmit antennas at the base station, currently standardized approaches would require a large percentage of the precious downlink and uplink resources in FDD massive MIMO be used for training signal transmissions and channel state information (CSI) feedback. To reduce the overhead of the downlink training phase, we propose practical open-loop and closed-loop training frameworks in this paper. We assume the base station and the user share a common set of training signals in advance. In open-loop training, the base station transmits training signals in a round-robin manner, and the user successively estimates the current channel using long-term channel statistics such as temporal and spatial correlations and previous channel estimates. In closed-loop training, the user feeds back the best training signal to be sent in the future based on channel prediction and the previously received training signals. With a small amount of feedback from the user to the base station, closed-loop training offers better performance in the data communication phase, especially when the signal-to-noise ratio is low, the number of transmit antennas is large, or prior channel estimates are not accurate at the beginning of the communication setup, all of which would be mostly beneficial for massive MIMO systems.