Convolutional neural network (CNN)-based deep learning (DL) has a wide variety of applications in the geospatial and remote sensing (RS) sciences, and consequently has been a focus of many recent studies. However, a review of accuracy assessment methods used in recently published RS DL studies, focusing on scene classification, object detection, semantic segmentation, and instance segmentation, indicates that RS DL papers appear to follow an accuracy assessment approach that diverges from that of traditional RS studies. Papers reporting on RS DL studies have largely abandoned traditional RS accuracy assessment terminology; they rarely reported a complete confusion matrix; and sampling designs and analysis protocols generally did not provide a population-based confusion matrix, in which the table entries are estimates of the probabilities of occurrence of the mapped landscape. These issues indicate the need for the RS community to develop guidance on best practices for accuracy assessment for CNN-based DL thematic mapping and object detection. As a first step in that process, we explore key issues, including the observation that accuracy assessments should not be biased by the CNN-based training and inference processes that rely on image chips. Furthermore, accuracy assessments should be consistent with prior recommendations and standards in the field, should support the estimation of a population confusion matrix, and should allow for assessment of model generalization. This paper draws from our review of the RS DL literature and the rich record of traditional remote sensing accuracy assessment research while considering the unique nature of CNN-based deep learning to propose accuracy assessment best practices that use appropriate sampling methods, training and validation data partitioning, assessment metrics, and reporting standards.