Abstract U-Th-Pb petrochronology is based on the incontrovertible fact that the diffusion of radiogenic Pb is negligibly small relative to retrograde reaction rates. Multi-element maps demonstrate that patchy textures tightly correspond to (U + Th)-Pb age variations, requiring that fluid-induced dissolution/ reprecipitation is the principal cause of Pb mobility. Attempts to model intracrystalline core-rim Pb zonations as diffusive transport are not legitimate unless genuine bell-shaped diffusion profiles in minerals can be documented, which happens only exceptionally. Monazite and zircon intra-grain age maps confirm that coupled dissolution-reprecipitation and retrogression reactions assisted by fluids control (Th + U)-Pb ages, not temperature. The chemical zonations observed in many (Th + U)-bearing mineral chronometers (e.g. monazite, allanite, xenotime, zircon) provide petrological constraints. Linking petrology with textures and the isotope record allows reconstructing entire segments of the P-T-A-X-D-t history of a rock and its geodynamic environment. The dearth of mathematically sound diffusion profiles equally applies to the isotope records of micas and feldspars. The tight link between petrology, microtextures, chemical composition and geochronology also pertains to Rb-Sr and K-Ar. Overdetermined multi-mineral Rb-Sr isochrons with excess scatter, and spatially resolved/stepwise release 39Ar-40Ar results, demonstrate ubiquitous correspondence between relict phases and isotopic inheritance. Many rock-forming minerals are highly retentive of Sr and Ar, unless they are obliterated by retrograde reactions. The rates of dissolution in fluid-controlled reactions are several orders of magnitude faster at upper and mid-crustal levels than diffusive reequilibration rates. Thus, as a rule Rb-Sr and K-Ar chronometers date their own formation. Accurately establishing P-T paths of monometamorphic rocks requires assessing petrologic equilibrium using multivariate thermodynamic software. Dating complex parageneses of polymetamorphic, unequilibrated rocks requires labor-intensive disentangling by: (i) qualitative identification of relicts, retrogression reactions, and chemically open systems by imaging techniques (e.g. cathodoluminescence, element maps, etc.); (ii) microchemical analyses at the μm-scale quantifying heterochemical disequilibrium phases and assigning them to a P-T-A-X segment; (iii) spatially resolved/stepwise release, relating the chemical signature of the analyzed mineral to its age. K-Ar and Rb-Sr usually provide a different perspective on the P-T evolution of a rock than does (Th + U)-Pb, as K + Rb-rich minerals (phyllosilicates and especially feldspars) mostly form later and react/dissolve faster in the retrograde path than U-rich accessory phases. The present paper reviews these general principles by means of well-understood examples, both successful and unsuccessful in matching the independently known external constraints.