Homologation reactions like the Kowalski ester homologation provide simple examples of insertion process in organic synthesis.  In the Arndt-Eistert reaction, a methylene unit is inserted into the carboxyl-carbon bond of carboxylic acid to form the next acid in the homologous series.  Organic Syntheses provides the example of t-BOC protected (S)-phenylalanine (2-amino-3-phenylpropanoic acid) being reacted sequentially with triethylamine, ethyl chloroformate, and diazomethane to produce the α-diazoketone, which is then reacted with silver trifluoroacetate / triethylamine in aqueous solution to generate the t-BOC protected form of (S)-3-amino-4-phenylbutanoic acid.
Mechanistically, the α-diazoketone undergoes a Wolff rearrangement to form a ketene in a 1,2-rearrangement. Consequently, the methylene group α- to the carboxyl group in the product is the methylene group from the diazomethane reagent.  The 1,2-rearrangement has been shown to conserve the stereochemistry of the chiral centre as the product formed from t-BOC protected (S)-phenylalanine retains the (S) stereochemistry with a reported enantiomeric excess of at least 99%.
A related transformation is the Nierenstein reaction in which a diazomethane methylene group is inserted into the carbon-chlorine bond of an acid chloride to generate an α-chloro ketone.  An example, published in 1924, illustrates the reaction in a substituted benzoyl chloride system:
Perhaps surprisingly, α-bromoacetophenone is the minor product when this reaction is carried out with benzoyl bromide, a dimeric dioxane being the major product. Organic azides also provide an example of an insertion reaction in organic synthesis and, like the above examples, the transformations proceed with loss of nitrogen gas.  When tosyl azide reacts with norbornadiene, a ring expansion reaction takes place in which a nitrogen atom is inserted into a carbon-carbon bond α- to the bridge head:
The Beckmann rearrangement is another example of a ring expanding reaction in which a heteroatom is inserted into a carbon-carbon bond. The most important application of this reaction is the conversion of cyclohexanone to its oxime, which is then rearranged under acidic conditions to provide ε-caprolactam, the feedstock for the manufacture of Nylon 6.  Annual production of caprolactam exceeds 2 billion kilograms.
Carbenes undergo both intermolecular and intramolecular insertion reactions.  Cyclopentene moieties can be generated from sufficiently long-chain ketones by reaction with trimethylsilyldiazomethane, (CH)Si–CHN:
Here, the carbene intermediate inserts into a carbon-hydrogen bond to form the carbon-carbon bond needed to close the cyclopentene ring.  Carbene insertions into carbon-hydrogen bonds can also occur intermolecularly:
Carbenoids  are reactive intermediates that behave similarly to carbenes.  One example is the chloroalkyllithium carbenoid reagent prepared in situ from a sulfoxide and t-BuLi which inserts into the carbon-boron bond of a pinacol boronic ester: