A number of lactose derivatives or analogs have been described that are useful for work with the lac operon.  These compounds are mainly substituted galactosides, where the glucose moiety of lactose is replaced by another chemical group.
* Isopropyl-β-D-thiogalactopyranoside (IPTG) is frequently used as an inducer of the lac operon for physiological work.  IPTG binds to repressor and inactivates it, but is not a substrate for β-galactosidase.  One advantage of IPTG for in vivo studies is that since it cannot be metabolized by E. coli. Its concentration remains constant and the rate of expression of lac p/o-controlled genes is not a variable in the experiment. IPTG intake is dependent on the action of lactose permease in P. fluorescens, but not in E. coli.
* Phenyl-β-D-galactose (phenyl-Gal) is a substrate for β-galactosidase, but does not inactivate repressor and so is not an inducer.  Since wild type cells produce very little β-galactosidase, they cannot grow on phenyl-Gal as a carbon and energy source.  Mutants lacking repressor are able to grow on phenyl-Gal.  Thus, minimal medium containing only phenyl-Gal as a source of carbon and energy is selective for repressor mutants and operator mutants.  If 10 cells of a wild type strain are plated on agar plates containing phenyl-Gal, the rare colonies which grow are mainly spontaneous mutants affecting the repressor.  The relative distribution of repressor and operator mutants is affected by the target size. Since the lacI gene encoding repressor is about 50 times larger than the operator, repressor mutants predominate in the selection.
* Thiomethyl galactoside [TMG] is another lactose analog. These inhibit the lacI repressor. At low inducer concentrations, both TMG and IPTG can enter the cell through the lactose permease. However at high inducer concentrations, both analogs can enter the cell independently. TMG can reduce growth rates at high extracellular concentrations.
* Other compounds serve as colorful indicators of β-galactosidase activity.
** ONPG is cleaved to produce the intensely yellow compound, orthonitrophenol and galactose, and is commonly used as a substrate for assay of β-galactosidase in vitro. 
** Colonies that produce β-galactosidase are turned blue by X-gal (5-bromo-4-chloro-3-indolyl-β-D-galactoside) which is an artificial substrate for B-galactosidase whose cleavage results in galactose and 4-Cl,3-Br indigo thus producing a deep blue color.
* Allolactose is an isomer of lactose and is the inducer of the lac operon.  Lactose is galactose-β(1→4)-glucose, whereas allolactose is galactose-β(1→6)-glucose. Lactose is converted to allolactose by β-galactosidase in an alternative reaction to the hydrolytic one.  A physiological experiment which demonstrates the role of LacZ in production of the "true" inducer in E. coli cells is the observation that a null mutant of lacZ can still produce LacY permease when grown with IPTG, a non-hydrolyzable analog of allolactose, but not when grown with lactose.  The explanation is that processing of lactose to allolactose (catalyzed by β-galactosidase) is needed to produce the inducer inside the cell.