The naked eye detection of single molecules in a complex mixture is the ultimate detection limit. Since a single molecule is unable to generate a strong enough signal, sensing methodologies able to reach that limit by necessity need to rely on signal amplification. This tutorial review describes various molecular approaches towards signal amplification in which a single analyte molecule affects the properties of a multitude of reporter molecules. Sensing by advanced instrumentation or changes in the physical properties of materials are excluded. The review is divided into four parts (catalysts, macromolecules, metal surfaces and supramolecular aggregates) depending on the species responsible for generating reporter molecules. Although on first sight apparently very diverse in nature, the majority of approaches rely on two key concepts: catalysis and multivalency. The ability of a catalyst to convert a multitude of substrate molecules into product (defined by the turn over number) makes a catalyst an intrinsic signal amplifier in case the chemical conversion of the substrate is accompanied by a measurable change in physical properties. For sensing purposes, catalytic activity must depend on the interaction between the analyte and the catalyst. Sensing using multivalent structures such as polymers and functionalized nanoparticles relies on the ability of a single analyte molecule to affect the properties of a multitude of reporter molecules collected in the multivalent structure. Chemical sensing systems will be discussed with detection limits that indeed go down to a few molecules and can rival the best biological assays. It will be shown that the most sensitive methods rely on a cascade of amplification mechanisms.