  Let $\lambda$ be a real number with $-\pi/2<\lambda<\pi/2.$ In order to study
$\lambda$-spirallike functions, it is natural to measure the angle according to
$\lambda$-spirals. Thus we are led to the notion of $\lambda$-argument. This
fits well the classical correspondence between $\lambda$-spirallike functions
and starlike functions. Using this idea, we extend deep results of Pommerenke
and Sheil-Small on starlike functions to spirallike functions. As an
application, we solved a problem given by Hansen in 1971.
