The term “landscape complexity” refers to the difficulty of understanding the spatial structure or functions of a landscape. Accordingly, there are two basic types of landscape complexity: spatial landscape complexity (that depends on geometry, entropy, randomness and topology) and functional landscape complexity (that depends on the complexity of interactions and flows of matter and energy in landscapes). Spatial landscape complexity is measurable by algorithmic methods that have been devised by the author, while functional landscape complexity is measurable by complex systems dynamics. Further, there is a range of algorithmic problems, models and theories that are useful in understanding and exploring both spatial and functional landscape complexities.