In the last 20 years, an increasing number of studies have been reported on membrane active peptides, which exert their biological activity by interacting with the cell membrane either to disrupt it and lead to cell lysis or to translocate through it to deliver cargos into the cell and reach their target. These peptides are attractive alternatives to currently used pharmaceuticals. Antimicrobial peptides (AMPs) and peptides designed for drug and gene delivery currently in the drug pipeline suggest that these membrane active peptides will soon constitute a significant percentage of the drug market. Here, we focus on two most prominent classes of membrane active peptides; AMPs and cell-penetrating peptides (CPPs). AMPs are a group of membrane active peptides that disrupt the membrane integrity or inhibit the cellular functions of bacteria, virus and fungi. CPPs are another group of membrane active peptides that mainly function as cargo-carriers even though they may also show antimicrobial activity to some extent. Biophysical techniques to understand how they interact with the membrane have shed light on the peptide-membrane interaction at various levels of detail. Structural investigation of membrane active peptides in the presence of the membrane provides important clues on the effect of the membrane environment on peptide conformations. Advances in live imaging techniques have allowed examination of peptide action at a single cell or single molecule level. In addition to these experimental biophysical techniques, molecular dynamics simulations provided clues on the peptide-lipid interactions and dynamics of the cell entry process at atomic detail. In this review, we summarize the recent advances in experimental and computational investigation of membrane active peptides with particular emphasis on two amphipathic membrane active peptides, the AMP melittin and the CPP pVEC.