The CRISPR-Cas9 system has become the most promising and versatile tool for genetic manipulation applications. Albeit the technology has been broadly adopted by both academic and pharmaceutic societies, the activity (on-target) and specificity (off-target) of CRISPR-Cas9 are decisive factors for any application of the technology. Several in silico gRNA activity and specificity predicting models and web tools have been developed, making it much more convenient and precise for conducting CRISPR gene editing studies. In this review, we present an overview and comparative analysis of machine and deep learning (MDL)-based algorithms, which are believed to be the most effective and reliable methods for the prediction of CRISPR gRNA on- and off-target activities. As an increasing number of sequence features and characteristics are discovered and are incorporated into the MDL models, the prediction outcome is getting closer to experimental observations. We also introduced the basic principle of CRISPR activity and specificity and summarized the challenges they faced, aiming to facilitate the CRISPR communities to develop more accurate models for applying.