Power spectral density vs Energy spectral density I read the following on Wikipedia:


  Power spectral density:
  
  The above definition of energy spectral density is most suitable for
  transients, i.e., pulse-like signals, for which the Fourier transforms
  of the signals exist. For continued signals that describe, for example, stationary physical processes, it makes more sense to define a power spectral density (PSD), which describes how the power of a signal or time series is distributed over the different frequencies, as in the simple example given previously.


I don't quite understand that paragraph. The first part says that "for some signals .. the Fourier transform does not exist". 


For which signals (in the context that we are discussing) does the Fourier transform not exist, and we therefore need to resort to the  PSD  rather than using the energy spectral density?
When obtaining the power spectral density, why can't we compute it directly? Why do we need to estimate it? 
Finally, on this topic, I have read about methods that use Kayser-windows when computing the PSD over time. What is the purpose of these windows in PSD estimation?
Random process is never ending, non-periodic phenomenon, so taking Fourier transform of its realizations makes no sense, not possible either. However if random process is stationary, then it is for sure that it has some finite power over some band of frequencies. Now, here the question arises that how to compute the power of this stationary random process, (fourier tranform is not possible to be taken directly)? So, what to do? we find the auto-correlation function of the given random process, whose fourier transform always exist. Finally, we take the fourier tranform of this autocorrelation function to get the power spectral density of the given stationary process.

If you integrate the power spectral density of a given stationary process over the interval from -$\infty$ to $\infty$ you ll get the total power contained in the given random process.