Proteins and peptides with hydrophobic and amphiphilic segments are responsible for many biological functions. The sensing and generation of membrane curvature are the functions of several protein domains or motifs. While some specific membrane proteins play an essential role in controlling the curvature of distinct intracellular membranes, others participate in various cellular processes such as clathrin-mediated endocytosis, where several proteins sort themselves at the neck of the membrane bud. A few membrane-inserting proteins form nanopores that permeate selective ions and water to cross the membrane. In addition, many natural and synthetic small peptides and protein toxins disrupt the membrane by inducing nonspecific pores in the membrane. The pore formation causes cell death through the uncontrolled exchange between interior and exterior cellular contents. In this article, we discuss the insertion depth and orientation of protein/peptide helices and their role as a sensor and inducer of membrane curvature as well as a pore former in the membrane. We anticipate that this extensive review will assist biophysicists to gain insight into curvature sensing, generation and pore formation by membrane insertion. Graphical Abstract: [Figure not available: see fulltext.]. © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.