Background: Cardiovascular diseases (CVDs) remain the leading global cause of mortality, yet a critical “translational gap” persists: Conventional biomarkers often fail to detect subclinical stages or predict individual disease trajectories. While single-omics studies have proliferated, the field lacks a unified framework synthesizing these molecular layers with advanced computational intelligence. Aim: This review addresses this gap by evaluating the synergistic integration of multi-omics and Artificial Intelligence (AI) to transition from descriptive markers toward predictive precision cardiology. Scope: Evidence from non-coding RNA networks (miRNAs, lncRNAs) and exosomal trafficking is synthesized alongside a critical assessment of Machine Learning (ML) architectures, including supervised, unsupervised, and deep learning (DL) models. Findings: Unlike traditional reviews, this work delineates the specific pipelines required to deconvolute high-dimensional signatures—such as TMAO, acylcarnitines, and cardiac-enriched miRNAs—into actionable risk models for heart failure (HF) and post-infarction outcomes. The primary barrier to clinical translation is identified not as data scarcity but as the lack of standardized bioinformatic workflows and model interpretability. Conclusions: This review distinguishes itself by proposing an integrated molecular–computational framework that prioritizes Explainable AI (XAI) and standardized multi-omic protocols. Such a shift is essential to bridge the gap between high-dimensional biological insights and routine clinical decision-making.