Robust statistics has traditionally focused on casewise outliers, meaning observations that behave differently from the bulk of the data. In modern datasets, however, contamination can occur in the form of cellwise outliers, which are individual contaminated entries in the data matrix. Even when the proportion of contaminated cells is relatively small, many observations may still contain at least one outlying value, which can make both classical and casewise robust methods unreliable. This talk presents recent developments for handling situations in which casewise and cellwise outliers appear simultaneously. We begin by introducing cellPCA, a novel robust principal component analysis method that estimates the principal subspace while simultaneously accommodating cellwise and casewise outliers, as well as missing values. Building on cellPCA, we then introduce cellRCov, which is a robust covariance estimator for high-dimensional settings. The second part of the talk focuses on multivariate linear regression. The cellMR estimator combines robust covariance estimation with regularization to handle outliers in both the predictor and response matrices. We then introduce cellBoot, a bootstrap procedure based on indirect inference that complements robust estimation with valid confidence intervals for the regression coefficients. We conclude with a perspective on more complex data structures and contamination patterns, including tensor data, time series, functional data, and blockwise contamination.