The main trend of modern data analysis is to reduce huge data bases to their low-dimensional approximations. Classical tool for this purpose is Principal Component Analysis (PCA). However it is sensitive to outliers and other deviations from standard assumptions. There are numerous approaches to robust PCA. We propose two novel models. One is based on minimization of Huber-like distances from low-dimensional subspaces. Simple and fast method for this convex optimization problem is proposed. The second is robust version of maximum likelihood method for covariance and location estimation for contaminated multivariate Gaussian distribution. Statistical validation of both approaches is an open problem.