Continuing crop domestication/redomestication and modification is a key determinant of the adaptation and fulfillment of the food requirements of an exploding global population under increasingly challenging conditions such as climate change and the reduction in arable lands. Monocotyledonous crops are not only responsible for approximately 70% of total global crop production, indicating their important roles in human life, but also the first crops to be challenged with the abovementioned hurdles; hence, monocot crops should be the first to be engineered and/or de novo domesticated/redomesticated. A long time has passed since the first green revolution; the world is again facing the challenge of feeding a predicted 9.7 billion people in 2050, since the decline in world hunger was reversed in 2015. One of the major lessons learned from the first green revolution is the importance of novel and advanced trait-carrying crop varieties that are ideally adapted to new agricultural practices. New plant breeding techniques (NPBTs), such as genome editing, could help us succeed in this mission to create novel and advanced crops. Considering the importance of NPBTs in crop genetic improvement, we attempt to summarize and discuss the latest progress with major approaches, such as site-directed mutagenesis using molecular scissors, base editors and especially homology-directed gene targeting (HGT), a very challenging but potentially highly precise genome modification approach in plants. We therefore suggest potential approaches for the improvement of practical HGT, focusing on monocots, and discuss a potential approach for the regulation of genome-edited products.