Semiconductor colloidal nanoplatelets (NPLs) are a promising new class of nanostructures that can bring much impact on lightning technologies, light-emitting diodes (LED), and laser fabrication. Indeed, great progress has been made in optimizing the optical properties of the NPLs for the visible spectral range, which has already made the implementation of a number of effective devices on their basis possible. To date, state-of-the-art near-infrared (NIR)-emitting NPLs are significantly inferior to their visible-range counterparts, although it would be fair to say that they received significantly less research attention so far. In this study, we report a comprehensive analysis of steady-state and time-dependent photoluminescence (PL) properties of four monolayered (ML) PbSe NPLs. The PL measurements are performed in a temperature range of 78–300 K, and their results are compared to those obtained for CdSe NPLs and PbSe quantum dots (QDs). We show that multiple emissive states, both band-edge and trap-related, are responsible for the formation of the NPLs’ PL band. We demonstrate that the widening of the PL band is caused by the inhomogeneous broadening rather than homogeneous one, and analyze the possible contributions to PL broadening.