CaZrF6 and CaHfF6 display much stronger negative thermal expansion (NTE) (alpha(L100 K) similar to -18 and -22 ppm K-1, respectively) than ZrW2O8 and other corner-shared framework structures. Their NTE is comparable to that reported for framework solids containing multiatom bridges, such as metal cyanides and metal-organic frameworks. However, they are formable as ceramics, transparent over a wide wavelength range and can be handled in air; these characteristics can be beneficial for applications. The NTE of CaZrF6 is strongly temperature-dependent, and first-principles calculations show that it is largely driven by vibrational modes below similar to 150 cm(-1). CaZrF6 is elastically soft with a bulk modulus (K-300K) of 37 GPa and, upon compression, starts to disorder at similar to 400 MPa. The strong NTE of CaZrF6, which remains cubic to <10 K, contrasts with cubic CoZrF6, which only displays modest NTE above its rhombohedral to cubic phase transition at similar to 270 K. CaZrF6 and CaHfF6 belong to a large and compositionally diverse family of materials, A(II)B(IV)F(6), providing for a detailed exploration of the chemical and structural factors controlling NTE and many opportunities for the design of controlled thermal expansion materials.