Superconducting nanowire single photon detectors (SNSPD) made from amorphous superconductors have showed great promise for achieving high fabrication yields, due to the highly uniform nature of the films. We present progress on the development of SNSPD based on amorphous MoSi with a critical temperature of around 5 K, which is ideal for detector operation at temperatures of 1 – 2.5 K, accessible with widely available cryogenic systems. First generation devices have achieved a saturated internal efficiency from visible to near-infrared wavelengths, which is the first requirement for high overall system efficiency. The broadband response has allowed us to make a robust study the energy-current relation in these devices, which defines the current required for a saturated internal detection efficiency for a given incident photon energy. Contrary to previous studies with other material systems, we find a nonlinear energy-current relation, which is an important insight into the detection mechanism in SNSPDs. The latest generation devices have been embedded into an micro-cavity structure in order to increase the system detection efficiency, which has increased to over 65% at 1550 nm. The efficiency is believed to be limited by fabrication imperfections and we present ongoing progress towards improving this characteristic as well as the yield of the devices. Efforts are also being made towards increasing the maximum operating temperature of the devices.