Two-dimensional (2D) noble-metal dichalcogenides exhibit exceptionally strong thickness-dependent bandgaps, which can be leveraged in a wide variety of device applications. A detailed study of their optical (e.g., optical bandgaps) and electrical properties (e.g., mobilities) is important in determining potential future applications of these materials. In this work, we perform detailed optical and electrical characterization of 2D PdSe2 nanoflakes mechanically exfoliated from a single-crystalline source. Layer-dependent bandgap analysis from optical absorption results indicates that this material is an indirect semiconductor with bandgaps of approximately 1.37 and 0.50 eV for the monolayer and bulk, respectively. Spectral photoresponse measurements further confirm these bandgap values. Moreover, temperature-dependent electrical measurements of a 6.8-nm-thick PdSe2 flake-based transistor show effective electron mobilities of 130 and 520 cm2 V-1 s-1 at 300 K and 77 K, respectively. Finally, we demonstrate that PdSe2 can be utilized for short-wave infrared photodetectors. A room-temperature specific detectivity (D) of 1.8 × 1010 cm Hz1/2 W-1 at 1 μm with a band edge at 1.94 μm is achieved on a 6.8-nm-thick PdSe2 flake-based photodetector.