Compositions and/or structures of degradable shape memory polymers (SMPs) ranging in form from neat/unfoamed to ultra low density materials of down to 0.005 g/cc density. These materials show controllable degradation rate, actuation temperature and breadth of transitions along with high modulus and excellent shape memory behavior. A method of making extremely low density foams (up to 0.005 g/cc) via use of combined chemical and physical blowing agents, where the physical blowing agents may be a single compound or mixtures of two or more compounds, and other related methods, including of using multiple co-blowing agents of successively higher boiling points in order to achieve a large range of densities for a fixed net chemical composition. Methods of optimization of the physical properties of the foams such as porosity, cell size and distribution, cell openness etc. of these materials, to further expand their uses and improve their performance.