Systems with many degrees of freedom cannot be described taxonomically (e.g., enumeration
of local energy minima in a glass or a protein). The statistical description of such systems will be
illustrated by means of two examples. One deals with the protein design problem, where the goal
is to find the sequence of amino acids that folds into a target structure. The sequence landscape
constructed by a flat-histogram Monte Carlo algorithm displays novel phase transitions in sequence
space, whose possible biological relevance remains an open question. In the second example,
the analysis of order in particle packings leads to the notion of an order map, in which the
state of the system is described by order parameters that quantify its statistical geometry. Striking
regularities emerge in the order map as the spectrum of liquid and glassy behavior ranging from
simple (atomic) to complex (associating) is traversed. The order map emerges as a useful organizing
principle in the study of structure, dynamics and thermodynamics of liquids and glasses.