$\mathrm{Y}\mathrm{V}{\mathrm{O}}_4:{\mathrm{Tm}}^{3+}$ crystals grown by the Czochralski technique and $\mathrm{Gd}\mathrm{V}{\mathrm{O}}_4:{\mathrm{Tm}}^{3+}$ and $\mathrm{Lu}\mathrm{V}{\mathrm{O}}_4:{\mathrm{Tm}}^{3+}$ crystals grown by the floating-zone technique were investigated using methods of optical spectroscopy. Polarized absorption and emission spectra were recorded at room temperature and at $6\mathrm{K}$. The crystal-field analysis was performed assuming the $D_{2\mathrm{d}}$ site symmetry for ${\mathrm{Tm}}^{3+}$ ions. In this way the missing crystal-field components of the ${}^{3}H_6$ ground multiplet were located. Room temperature absorption spectra were analyzed in the framework of the Judd-Ofelt theory. Evaluated radiative lifetimes of luminescent levels of ${\mathrm{Tm}}^{3+}$ follow a general trend diminishing in agreement with the sequence: $\mathrm{Y}\mathrm{V}{\mathrm{O}}_4:{\mathrm{Tm}}^{3+}\to \mathrm{Gd}\mathrm{V}{\mathrm{O}}_4:{\mathrm{Tm}}^{3+}\to \mathrm{Lu}\mathrm{V}{\mathrm{O}}_4:{\mathrm{Tm}}^{3+}$. Luminescence lifetimes measured for the systems under study are similar except for the ${}^{3}F_4$ lifetime, which appears to be surprisingly short for $\mathrm{Lu}\mathrm{V}{\mathrm{O}}_4:{\mathrm{Tm}}^{3+}$. Anisotropy of optical spectra is particularly pronounced in $\mathrm{Lu}\mathrm{V}{\mathrm{O}}_4:{\mathrm{Tm}}^{3+}$. Peak absorption cross section for the band relevant for optical pumping at about $805\mathrm{nm}$ is roughly three times higher for $\pi$ polarization. Stimulated emission cross sections for the ${}^{3}F_4\text{−}{}^{3}H_6$ transition near $1800\mathrm{nm}$ were evaluated using the reciprocity method. The diode-pumped continuous wave laser operation in $\mathrm{Gd}\mathrm{V}{\mathrm{O}}_4:{\mathrm{Tm}}^{3+}$ with a slope efficiency of up to 40% is demonstrated. In $\mathrm{Lu}\mathrm{V}{\mathrm{O}}_4:{\mathrm{Tm}}^{3+}$ the diode-pumped laser oscillation in a pulsed mode was observed.