  Firstly, the Markovian stochastic Schr\"odinger equations are presented,
together with their connections with the theory of measurements in continuous
time. Moreover, the stochastic evolution equations are translated into a
simulation algorithm, which is illustrated by two concrete examples - the
damped harmonic oscillator and a two-level atom with homodyne photodetection.
Then, we consider how to introduce memory effects in the stochastic
Schr\"odinger equation via coloured noise. Specifically, the approach by using
the Ornstein-Uhlenbeck process is illustrated and a simulation for the
non-Markovian process proposed. Finally, an analytical approximation technique
is tested with the help of the stochastic simulation in a model of a
dissipative qubit.
