Large single crystals of rare-earth rhenium aluminide RRe2Al10, with R=Y, and Gd–Lu were grown out of an Al-rich solution. Single crystal x-ray diffraction data confirmed the orthorhombic Cmcm structure for all members: R=Gd-Dy with TbRe2Al10-structure type (formula unit per cell Z=8); R=Y, and Ho–Lu with LuRe2Al10-structure type (Z=12). There is no evidence of a localized 3d electron moment in R=Y and Lu; R=Yb is nonmagnetic down to 1.8 K, but develops an enhanced electronic specific heat of ∼95 mJ mol−1 K−2. Ordering temperatures range from ferromagnetic order in R=Gd with Tc=7.2(1) K, antiferromagnetic order in R=Tbat TN=5.0(3) K, to R=Dy, Ho, and Er giving magnetic ordering temperatures of Tmag=1.7(1), ≤0.4, and 1.1(2) K, respectively. All compounds have effective moments close in value to that of free R3+ at high temperatures.