There exist vector Gaussian interference channels that may not satisfy the strong interference condition but for which the capacity can still be achieved by jointly decoding the signal and the interference. This kind of interference is called generally strong interference. Sufficient conditions for a vector Gaussian interference channel to have generally strong interference are derived. The sum-rate capacity and the boundary points of the capacity region are also determined. Furthermore, new sufficient conditions for a vector Gaussian interference channel to achieve the sum-rate capacity by treating interference as noise are derived, which generalize all the existing results. Some boundary points on the capacity region of a vector Z interference channel under noisy interference are also determined to be achieved by treating interference as noise.