The heart has frequent and robust elevations of cytosolic calcium ([Ca2+]i) that underlie each contraction. Ca2+ release originates from thousands of Ca2+ release units (CRUs) distributed throughout the cardiomyocyte which can generate localized Ca2+ elevations, Ca2+ sparks, that are synchronized during excitation-contraction (EC) coupling to produce the global [Ca2+]i transient. Positioned in close proximity (~ 100 nm) to these CRUs are the intramyofibrillar mitochondria (IFMs) which are briefly (10--20 ms) exposed to microdomains of high [Ca2+ ]i (1--10 microM) during Ca2+ release. Elevated [Ca2+]i coupled with the highly polarized inner mitochondrial membrane (IMM) potential (DeltaPsim ≈ --180 mV) creates a powerful electrochemical driving force for Ca 2+ uptake through the mitochondrial Ca2+ uniporter (MCU) complex. Low "physiological" mitochondrial matrix Ca 2+ ([Ca2+]m) (~0.1--10 microM) is thought to regulate metabolism via oxidative phosphorylation, while "pathophysiological" [Ca2+]m overload (> 10 microM) leads to necrotic cell death. To date, the biophysical details surrounding the magnitude and regulation of mitochondrial Ca2+ uptake remain poorly understood, with the functional significance of [Ca2+]m signals providing further controversy. Three independent studies are provided in this thesis that look to improve our quantitative understanding of "local control" of [Ca2+]i signaling, the regulation and magnitude of [Ca2+]m signals, and the mechanism by which [Ca2+]m contributes to dynamic mitochondrial adenosine triphosphate (ATP) synthesis. The first study tests the hypothesis that "stable and synchronous release of local [Ca2+] i signals relies on physiological Ca2+ sensitivity of the ryanodine receptor". The second study tests the hypothesis that "mitochondrial Ca2+ uptake is under thermodynamic control to yield the small alterations in [Ca2+]m during EC coupling." The final study tests the hypothesis that "[Ca2+]m regulates ATP production through altering the thermodynamic driving force for ATP synthesis". The novel quantitative results provided herein help to clarify and constrain our understanding of EC coupling and the role of Ca2+ in the mitochondrial matrix.