Materials with short-wave infrared (SWIR) emission are promising contrast agents for in vivo animal imaging, providing high-contrast and high-resolution images of blood vessels in deep tissues. However, SWIR emitters have not been developed as molecular labels for microscopy applications in the life sciences, which require optimized probes that are bright, stable, and small. Here, we design and synthesize semiconductor quantum dots (QDs) with SWIR emission based on HgxCd1-xSe alloy cores red shifted to the SWIR by epitaxial deposition of thin HgxCd1-xS shells with a small band gap. By tuning alloy composition alone, the emission can be shifted across the visible-to-SWIR (VIR) spectra while maintaining a small and equal size, allowing direct comparisons of molecular labeling performance across a broad range of wavelength. After coating with click-functional multidentate polymers, the VIR-QD spectral series has high quantum yield in the SWIR (14-33%), compact size (13 nm hydrodynamic diameter), and long-term stability in aqueous media during continuous excitation. We show that these properties enable diverse applications of SWIR molecular probes for fluorescence microscopy using conjugates of antibodies, growth factors, and nucleic acids. A broadly useful outcome is a 10-55-fold enhancement of the signal-to-background ratio at both the single-molecule level and the ensemble level in the SWIR relative to visible wavelengths, primarily due to drastically reduced autofluorescence. We anticipate that VIR-QDs with SWIR emission will enable ultrasensitive molecular imaging of low-copy number analytes in biospecimens with high autofluorescence.