We explain the multivariate regular variation and a tail dependence measure "extremogram and cross-extremogram", taking a bivariate GARCH model as an example. We show that the tails of the components of a bivariate GARCH(1,1) process may exhibit power law behavior but, depending on the choice of the parameters, the tail indices of the components may differ. Then, we derive asymptotic theory for the extremogram and cross-extremogram of a bivariate GARCH(1,1) process. Moreover, we discuss what GARCH models can and cannot do in terms of the tail modeling, while comparing stochastic volatility models. We also mention limitations of the current notion of multivariate regular variation and we pose several problems to be solved.