Colloidal quantum dots (QDs) emitting in the infrared (IR) are promising building blocks for numerous photonic, optoelectronic and biomedical applications owing to their low-cost solution-processability and tunable emission. Among them, lead- and mercury-based QDs are currently the most developed materials. Yet, due to toxicity issues, the scientific community is focusing on safer alternatives. In this regard, indium arsenide (InAs) QDs are one of the best candidates as they can absorb and emit light in the whole near infrared spectral range and they are RoHS-compliant, with recent trends suggesting that there is a renewed interest in this class of materials. This review focuses on colloidal InAs QDs and aims to provide an up-to-date overview spanning from their synthesis and surface chemistry to post-synthesis modifications. We provide a comprehensive overview from initial synthetic methods to the most recent developments on the ability to control the size, size distribution, electronic properties and carrier dynamics. Then, we describe doping and alloying strategies applied to InAs QDs as well as InAs based heterostructures. Furthermore, we present the state-of-the-art applications of InAs QDs, with a particular focus on bioimaging and field effect transistors. Finally, we discuss open challenges and future perspectives.