Because 50% of heart failure hospital admissions have diastolic heart failure (DHF) quantifying diastolic function (DF) has reached new prominence. Conventionally DF indices have been computed from shape-based features (height, duration, area) of Doppler waveforms such as the E-wave, (transmitral flow velocity), or E'-wave (mitral annular velocity) without regard to causal mechanisms. Solution of the 'inverse problem' has been achieved via the parametrized diastolic filling (PDF) formalism, a linear, kinematic model which treats the elastic, recoil-driven suction-pump attribute of the left ventricle as a damped simple harmonic oscillator (SHO). PDF uses the E-wave as input and generates stiffness (k), relaxation/ damping (c) and load (x0) as output. Scientific successes include the prediction that filling must be driven by a linear, bi-directional spring, later validated as a property of the giant cardiac protein titin, which generates a recoiling force at the cellular level in early diastole. Selected recent kinematic modeling achievements include: explanation why E-wave deceleration time must be determined jointly by stiffness (k) and relaxation (c), rather than by stiffness alone; LV equilibrium volume is the volume at diastasis; solution of the load-independent index of diastolic function (LIIDF) problem; solution of the isovolumic pressure decay (IVPD) problem. Clinical application reveals that contrary to dogma, chamber relaxation/viscoelasticity (PDF parameter c) rather than chamber stiffness (PDF parameter k) most often differentiates between controls vs. diastolic dysfunction subjects, thereby providing mechanistic insights into DHF.