The major breakthroughs as far as Mechanical Engineering is concerned are in field of Acoustics and Mechatronics.
Recently FloDesign Sonics has developed a uniquely effective patented technology called Acoustic Wave Separation (AWS) that separates or cleans water or other liquids from other contaminants. It cleans all the contaminants like radioactive material, hydrocarbons, bacteria, chemical additives, salt, and more, without the use of chemicals or filters.
In field of Mechatronics and Robotics it's the development of Humanoid robots like SOPHIA developed by Hanson Robotics.
The previously mentioned breakthroughs can be viewed in field intersecting with Mechanical Engineering. As such, current and future outstanding solutions will require interdisciplinary knowledge of Smart and Composite Materials Science, AI and Computer Sciences, and Mechatronics implementations of which are found in Aeronautics and such as Smart UAV/MAV, Future Aircraft Concepts (see BWB, Hybrid and ALL-Electric) and nano vehicles for medical applications, humanoid robotics and etc.