Ontologies are widely used in various domains, including biomedical research, to structure information, represent knowledge, and analyze data. The combination of ontologies from different domains is crucial for systematic data analysis and comparison of similar domains. This process requires ontology composition, integration, and alignment, which involve creating new classes by reusing classes from different domains, aggregating types of ontologies within the same domain, and finding correspondences between ontologies within the same or similar domain. This thesis presents use cases where we applied ontology composition, integration, and alignment of phenotype ontologies, and evaluated the resulting ontologies and alignment. First, we analyzed a large aging dataset of inbred laboratory mice, using Mouse Anatomy and Mouse Pathology ontologies. Second, we integrated phenotype ontologies for human and model organism phenotypes to enable comparisons of phenotypes between and within individual species. We developed Pheno-e, an extension of PhenomeNet. We identified novel abnormal anatomical classes for fly phenotypes, allowing the annotation of fly genes that were not annotated before. We demonstrate the distinct contributions of each species' phenotypic data to detecting human diseases using Pheno-e, and show that mouse phenotypic data contributes the most to the discovery of gene--disease associations. This work could guide the selection of model organisms when building methods to find gene-disease associations. Additionally, we refined class definitions in phenotypic ontologies, specifically targeting cell cardinality phenotypes. This representation resolved incorrect inferences in the utilized ontologies, enabling accurate interpretation of phenotypic descriptions. Our findings reveal that this correction enhances gene-disease prediction for diseases associated with cardinality phenotypes. Third, we introduce a novel neural-symbolic method that combines logic fundamentals with machine learning for ontology alignment. This method begins with symbolic representation, followed by iterative neural learning for alignment and symbolic representation consistency checking and reasoning, and back to neural learning. We demonstrate that our system generates noncontroversial alignments first and these alignments are coherent with respect to OWL EL. This novel method can pave the way for more accurate and efficient ontology-based methods, which can have significant implications for various semantic web applications.