The thermoplastic polyurethane compositions described herein have very good recovery properties, rebound resilience, or both, while also having good softness (i.e. low hardness). It has been difficult to provide thermoplastic polyurethane compositions with this combination of properties. Some compositions described herein also provide low haze and/or good clarity properties. These combination of properties make the thermoplastic polyurethane compositions described herein useful materials for application that require fast recovery, good rebound resilience, or both while also requiring soft materials, and in some embodiments low haze and/or good clarity.