Myocardial and aortic stiffness are increasingly recognized as clinically relevant biomarkers for cardiovascular disease, yet their noninvasive quantification remains challenging. Magnetic resonance elastography (MRE) has emerged as a promising technique for the spatial mapping of tissue biomechanics by visualizing and analyzing propagating shear waves. This narrative review summarizes the current state of cardiovascular MRE, spanning technical developments in wave generation (acoustic, electromagnetic, gravitational, and transducer-free approaches), pulse sequence design (echo-planar imaging, gradient-recalled echo, spiral, and free-breathing three-dimensional acquisitions), and inversion algorithms (local frequency estimation, direct inversion, finite element methods, and multifrequency elastography). We present evidence from phantom validation, animal models (myocardial infarction, hypertension, right ventricular hypertrophy), and human studies encompassing cardiac amyloidosis, hypertrophic cardiomyopathy, diastolic dysfunction, and abdominal aortic aneurysm. Additionally, we discuss current challenges, including waveguide effects, standardization needs, and clinical translation barriers, and highlight emerging solutions through artificial intelligence, multifrequency methods, and transducer-free cardiac MRE.