Multimodal large language models (MLLMs) can generate fluent responses but may overlook relevant evidence or violate task and safety constraints. This survey examines MLLM alignment through two complementary gaps: the Modality Gap, concerning cross-modal correspondence and the use of task-relevant evidence, and the Intent Gap, concerning behavior relative to specified goals, constraints, and human expectations. We organize the literature along six dimensions: architecture, objective functions, data construction, training, evaluation, and applications. Across these dimensions, we link alignment mechanisms and supervision assumptions to the failures they target and the evidence supporting their effectiveness. Our analysis clarifies what interface compatibility, target imitation, preference learning, and verifiable rewards can each demonstrate about alignment, together with the limitations of their underlying supervision. We further summarize evaluation at the representation, task, and behavior levels, emphasizing evidence dependence, constraint compliance, and the distinction between observed improvements and explanations of their underlying mechanisms. Applications in robotics, safety, healthcare, recommendation, and climate decision support reveal three recurring requirements: traceable evidence, valid supervision, and decisions that respect domain constraints. Building on this synthesis, we identify four research directions: evidence-consistent alignment across modalities, verified self-correction and test-time alignment, diagnosis-guided repair, and reliable transfer to underrepresented settings.