During the past several decades, research on human faces has always been active. In this thesis, we focus on two challenging yet meaningful visual tasks, age estimation and age-invariant face recognition, both of which are based on captured facial images. At first, regarding age estimation, we summarize the associate challenges mainly come from two aspects, uncertainty and certainty. To be more specific, the uncertainty issue refers to the facial aging process is commonly affected by age-independent factors, such ad gender, race, health condition, etc. The certainty means expectable but non- linear aging process on the face: our appearance mainly develops in facial skeletons be- fore physiological maturity. After that, it goes into a relatively stable phase and mostly changes in the surface level (i.e., skin). In order to alleviate the uncertain impacts from those age-unrelated factors, we first design a generic framework based on the proba- bilistic model. Our method simultaneously estimates the occurrence probabilities of conditions determined by those affecting factors and corresponding conditional ages. The mathematical expectation of them is taken as the final age prediction. On the other hand, we introduce two new approaches to deal with the certainty challenge. In this solution, we confront the mathematical essence of the age estimation task, namely, the ordinal regression/classification problem, and construct two particular ordinal ensembles, respectively. The superiority of our two ensembles against existing competitors is verified by both theoretical analysis and practical evaluation. Then we introduce a new approach to extract effective features for recognizing faces across ages. It is characterized by implicit and explicit feature purification mechanisms, which encourage the network model to generate age-insensitive and identity-discriminative facial representations. Finally, we briefly conclude this thesis and show future research directions.