Cardiovascular disease (CVD), the leading cause of death today, incorporates a wide range of cardiovascular system malfunctions that affect heart functionality. It is believed that the hemodynamic loads exerted on the cardiovascular system, the left ventricle (LV) in particular, are the leading cause of CVD initiation and propagation. Moreover, it is believed that the diagnosis and prognosis of CVD at an early stage could reduce its high mortality and morbidity rate. Therefore, a set of robust clinical cardiovascular assessment tools has been introduced to compute the cardiovascular hemodynamics in order to provide useful insights to physicians to recognize indicators leading to CVD and also to aid the diagnosis of CVD. Recently, a combination of computational fluid dynamics (CFD) and different medical imaging tools, image-based CFD (IB-CFD), has been widely employed for cardiovascular functional assessment by providing reliable hemodynamic parameters. Even though the capability of CFD to provide reliable flow dynamics in general fluid mechanics problems has been widely demonstrated for many years, up to now, the clinical implications of the IB-CFD patient-specific LVs have not been applicable due to its limitations and complications. In this paper, we review investigations conducted to numerically simulate patient-specific human LV over the past 15 years using IB-CFD methods. Firstly, we divide different studies according to the different LV types (physiological and different pathological conditions) that have been chosen to reconstruct the geometry, and then discuss their contributions, methodologies, limitations, and findings. In this regard, we have studied CFD simulations of intraventricular flows and related cardiology insights, for (i) Physiological patient-specific LV models, (ii) Pathological heart patient-specific models, including myocardial infarction, dilated cardiomyopathy, hypertrophic cardiomyopathy and hypoplastic left heart syndrome. Finally, we discuss the current stage of the IB-CFD LV simulations in order to mimic realistic hemodynamics of patient-specific LVs. We can conclude that heart flow simulation is on the right track for developing into a useful clinical tool for heart function assessment, by (i) incorporating most of heart structures' (such as heart valves) operations, and (ii) providing useful diagnostic indices based hemodynamic parameters, for routine adoption in clinical usage.