Calcium phosphate compositions that are particularly useful and unique as orthopedic and dental cements and remineralizers, as well as methods and kits for their use, and the resulting products are disclosed. The compositions comprise tetracalcium phosphate which has been prepared from a mixture with a calcium to phosphorous ratio of less than 2, or prepared and maintained under substantially anhydrous conditions prior to use or, preferably, both. The novel compositions are converted substantially to hydroxyapatite upon setting, are substantially gradually resorbable and replaced by bone when implanted in contact with living bony tissue, and offer distinct advantages in terms of cement strength, setting time and reliability and other properties.