Adequate access to affordable, healthy food has long been a public health concern and has become a more pressing societal issue following the Great Recession and rising incidents of diet-related diseases. In response, research and government efforts have largely focused on identifying disadvantaged areas with poor food access and formulating policies to improve accessibility. However, the approaches that have been widely relied upon by researchers and practitioners for food access assessment are severely flawed, which may lead to inconsistent research findings or neglect of the needs of under-served/un-served neighborhoods. This dissertation identifies three important aspects of food access for improvement: the appropriate scale/neighborhoods for analysis, the use of food outlets as a proxy for affordable, healthy food; and the assessment method. In particular, three studies are conducted to: (1) examine how varying spatial scales and aggregation methods affect accessibility assessments; (2) explore the role of independent grocers, which have been neglected in previous food access studies as elements of the food landscape that may change the perception of food deserts; and (3) investigate how individual-level food access patterns compare to the widely used, area-based neighborhood measures of expected accessibility. While the dissertation discusses and addresses theoretical challenges in food access, the empirical studies conducted in the Tucson, Arizona metropolitan area contribute to a better understanding of the real-world complexity of food access. The results shed light on some predicaments identified in recent studies and have important policy implications for how best to efficiently and effectively design strategies and initiatives to enhance food-provision access.