The first reported click reaction, copper(I)-catalyzed azide-alkyne 1,3-dipolar cycloaddition had limited biocompatibility due to the high toxicity of copper. Since alternative bioorthogonal click reactions have been developed, they have strongly influenced the field of chemical biology. Here are summarized three main metal-free click methodologies based on cycloaddition, Staudinger and thio-ene reactions. This review contains the basic principles, some mechanistic considerations and a collection of reagents that can be used in each method. Firstly, Diels-Alder and strain promoted inverse electron demand Diels-Alder cycloadditions are outlined together with triazole and isoxazole formation by 1,3-dipolar cycloadditions. Secondly, Staudinger-Bertozzi ligation, a chemoselective reaction of azides and engineered triarylphosphines, is discussed. Finally, thio-click chemistries including thiol-ene, thiol-yne, thio-Michael and fluoro-thio-click reactions are reviewed. Among the most important bioapplications of these click methodologies is the labeling of glycans, proteins, lipids and DNA. Additionally, synthetic methods and surface immobilization of biomolecules and biologically useful polymeric materials are also reviewed.