Reading a scheme

Start with the conditions. A strong base, an acid, a metal, a peroxide: the reagent line narrows the reaction type before you look at a single bond.
Find what changed. Compare starting material and product atom by atom: which bond formed, which left, and whether the carbon count grew.
Substitution vs. elimination vs. addition is a bookkeeping question: same number of σ bonds, fewer, or more.
Mechanism follows structure. A tertiary or benzylic center with a weak nucleophile points to a cation; a primary center with a strong nucleophile does not.
Every example here is a real reaction with a real citation. The yields are the authors’ own.

Horner–Wadsworth–Emmons reaction

4 real reactions from the literature, on phosphonate esters and thioesters. Each scheme shows starting materials, conditions and products, with the yield and reference where the source reports them.

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Horner–Wadsworth–Emmons: triethyl phosphonoacetate (a phosphonate ester) and pyruvic aldehyde dimethyl acetal (a methyl ketone) with 1) K2CO3 / H2O; 2) HCl / H2O gives ethyl (2E)-3-methyl-4-oxo-2-butenoate (the (E)-alkene). 85% yield.

Horner–Wadsworth–EmmonsJ. Am. Chem. Soc. 2004, 126, 5984
Horner–Wadsworth–Emmons: methyl diethylphosphonoacetate (a phosphonate ester) with 1); 2) gives methyl (E)-4,4-dimethyl-5-oxohept-2-enoate (the (E)-alkene). 83% yield.

Horner–Wadsworth–EmmonsOrg. Lett. 2008, 10, 1183
Horner–Wadsworth–Emmons: hydroxyacetone (a methyl ketone) and diethyl (cyanomethyl)phosphonate (a phosphonate ester) with 2 equiv LiOH gives (e)-4-hydroxy-3-methylbut-2-enenitrile (the (E)-alkene). 86% yield.

Horner–Wadsworth–EmmonsTetrahedron Lett. 2003, 44, 1333
Horner–Wadsworth–Emmons: a thioester with 1) DIBAL-H; 2) gives the (E)-alkene.

Horner–Wadsworth–EmmonsRealOChem worksheet