In the last 20 years, an increasing number of studies have been reported on membrane active peptides. These peptides 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. Membrane active peptides are attractive alternatives to currently used pharmaceuticals and the number of antimicrobial peptides (AMPs) and peptides designed for drug and gene delivery in the drug pipeline is increasing. Here, we focus on two most prominent classes of membrane active peptides; AMPs and cell-penetrating peptides (CPPs). Antimicrobial peptides are a group of membrane active peptides that disrupt the membrane integrity or inhibit the cellular functions of bacteria, virus, and fungi. Cell penetrating peptides are another group of membrane active peptides that mainly function as cargo-carriers even though they may also show antimicrobial activity. Biophysical techniques shed light on peptide-membrane interactions at higher resolution due to the advances in optics, image processing, and computational resources. 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. Live imaging techniques allow examination of peptide action at a single cell or single molecule level. In addition to these experimental biophysical techniques, molecular dynamics simulations provide 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.