  Quadratic variations of Gaussian processes play important role in both
stochastic analysis and in applications such as estimation of model parameters,
and for this reason the topic has been extensively studied in the literature.
In this article we study the problem for general Gaussian processes and we
provide sufficient and necessary conditions for different types of convergence
which include convergence in probability, almost sure convergence,
$L^p$-convergence as well as convergence in law. Furthermore, we study general
Gaussian vectors from which different interesting cases including first or
second order quadratic variations can be studied by appropriate choice of the
underlying vector. Finally, we provide a practical and simple approach to
attack the problem which simplifies the existing methodology considerably.
