VaR usually assumes normally distributed returns (historical VaR is a different issue). That's often not realistic. This is particularly problematic for alternative investments which often exhibit skewness and kurtosis (i.e. found in non-normal return distributions). It fails to consider path dependency issues. It fails to express the magnitude of loses in the tail. VaR doesn't consider correlations properly (subject to estimation error) so may over/under state risk. Specifically, VaR isn't said to be additive, one portfolio's VaR added to another portfolio's VaR will unlikely sum to the combined VaR. Different measures of VaR can yield different outcomes - so there's a lack of consistency. VaR is subject to garbage in; garbage out data errors. VaR is difficult to calculate if there are too many assets to measure. Hope that helps.
