Generative artificial intelligence (GenAI) has become a transformative approach in bioinformatics that often enables advancements in genomics, proteomics, transcriptomics, structural biology, and drug discovery. To systematically identify and evaluate these growing developments, this review proposed six research questions (RQs), according to the preferred reporting items for systematic reviews and meta-analysis methods. The objective is to evaluate impactful GenAI strategies in methodological advancement, predictive performance, and specialization, and to identify promising approaches for advanced modeling, data-intensive discovery, and integrative biological analysis. RQ1 highlights diverse applications across multiple bioinformatics subfields (sequence analysis, molecular design, and integrative data modeling), which demonstrate superior performance over traditional methods through pattern recognition and output generation. RQ2 reveals that adapted specialized model architectures outperformed general-purpose models, an advantage attributed to targeted pretraining and context-aware strategies. RQ3 identifies significant benefits in the bioinformatics domains, focusing on molecular analysis and data integration, which improves accuracy and reduces errors in complex analysis. RQ4 indicates improvements in structural modeling, functional prediction, and synthetic data generation, validated by established benchmarks. RQ5 suggests the main constraints, such as the lack of scalability and biases in data that impact generalizability, and proposes future directions focused on robust evaluation and biologically grounded modeling. RQ6 examines that molecular datasets (such as UniProtKB and ProteinNet12), cellular datasets (such as CELLxGENE and GTEx) and textual resources (such as PubMedQA and OMIM) broadly support the training and generalization of GenAI models.