Why Do we need a right-continuous filtration with $\mathcal{F}_0$ containing all P-null sets?

Question

When we consider a Stochastic Differential Equation we let $(\Omega,\mathcal F, \{\mathcal F_t\}_{t\ge 0},P )$ be a complete probability space with a filtration $\{\mathcal F_t\}_{t\ge 0}$ satisfying the usual conditions, i.e. it is right continuous and $\mathcal F_0$ contains all $P$-null sets.

Why are these "usual" conditions important ? What if we omit them ?