Polygonal knot space is the smooth manifold of embeddings of n-sided polygons in three-space. Specific spaces are required to respect additional structure such as the number or length of edges, bounds on the angles between adjacent edges, bounds on the distance between non-adjacent edges, etc. Methods and results pertaining to the space of equilateral knots and its position in the space of polygonal knots will be presented. An associated focus will be the physical characteristics of equilateral knots such as their optimal energy, ropelength or thickness, diameter, or convex hull volume.