We shall start with an introduction to general stochastic differential equations with memory, also called stochastic delay differential equations (SDDE), and present some of their basic properties. Then we turn to affine SDDE's of the form
dX(t) = \int_{-r}^0 X(t+s)a(ds)dt + dW(t) (1)
where a(.) is an arbitrary finite signed measure on [-r,0] and W(.) is a standard Wiener process. For (1) several special mathematical tools can be derived, which allow to study the behaviour of the solutions of (1). Conditions on a(.) are given under which (1) allows a stationary solution. The case that W(.) is substituted by a Levy process is considered for the question of stationarity also.