Today's industry is flooded with tracking data originating from vessels across the globe that transmit their position at frequent intervals. These voluminous and high-speed streams of data has led researchers to develop novel ways to compress them in order to speed-up processing without losing valuable information. To this end, several algorithms have been developed that try to compress streams of vessel tracking data without compromising their spatio-temporal and kinematic features. In this paper, we present a wide range of several well-known trajectory compression algorithms and evaluate their performance on data originating from vessel trajectories. Trajectory compression algorithms included in this research are suitable for either historical data (offline compression) or real-time data streams (online compression). The performance evaluation is three-fold and each algorithm is evaluated in terms of compression ratio, execution speed and information loss. Experiments demonstrated that each algorithm has its own benefits and limitations and that the choice of a suitable compression algorithm is application-dependent. Finally, considering all assessed aspects, the Dead-Reckoning algorithm not only presented the best performance, but it also works over streaming data, which constitutes an important criterion in maritime surveillance.