The human cerebral cortex undergoes dramatic and critical development during early postnatal stages. Benefiting from advances in neuroimaging, many infant brain magnetic resonance imaging (MRI) datasets have been collected from multiple imaging sites with different scanners and imaging protocols for the investigation of normal and abnormal early brain development. However, it is extremely challenging to precisely process and quantify infant brain development with these multisite imaging data because infant brain MRI scans exhibit (a) extremely low and dynamic tissue contrast caused by ongoing myelination and maturation and (b) inter-site data heterogeneity resulting from the use of diverse imaging protocols/scanners. Consequently, existing computational tools and pipelines typically perform poorly on infant MRI data. To address these challenges, we propose a robust, multisite-applicable, infant-tailored computational pipeline that leverages powerful deep learning techniques. The main functionality of the proposed pipeline includes preprocessing, brain skull stripping, tissue segmentation, topology correction, cortical surface reconstruction and measurement. Our pipeline can handle both T1w and T2w structural infant brain MR images well in a wide age range (from birth to 6 years of age) and is effective for different imaging protocols/scanners, despite being trained only on the data from the Baby Connectome Project. Extensive comparisons with existing methods on multisite, multimodal and multi-age datasets demonstrate superior effectiveness, accuracy and robustness of our pipeline. We have maintained a website, iBEAT Cloud, for users to process their images with our pipeline ( http://www.ibeat.cloud ), which has successfully processed over 16,000 infant MRI scans from more than 100 institutions with various imaging protocols/scanners.