A precise mathematical definition is given for spiral plane tilings. It is not restricted to monohedral tilings and is tested on a series of examples from the literature. Unwanted cases from regular tilings can be excluded. In case of one single arm a modified definition can be applied. Also the special case of locally infinite tilings with one singular point can be treated with any number of spiral arms. The question whether such a definition in mathematical terms could be given was posed by Grünbaum and Shephard in the late 1970s.