While I cannot specifically pin point to any one, efforts at keeping the sea level rise from impacting coastal cities would be a major challenge. The Japanese built a sea wall which failed. Now they are on to a different method of controlling coastal flooding by envisioning floating cities. A recent PBS show on "Sinking Cities" outlined the problems due to sea level rise in the coastal cities of New York, London , Miami and Tokyo and the engineering efforts to mitigate the flooding impact on the population.
Getting energy from our infra-red planet radiation: a current Harvard research https://www.seas.harvard.edu/news/2014/03/infrared-new-renewable-energy-source Saudis managed to create a diode that generate electricity using infra-red https://interestingengineering.com/researchers-create-diode-that-generates-electricity-using-infrared-energy
Creating a large battery system that could stand a million-volts shock and that way, get energy from lightnings bolts. (for what I know, this isn't a current research, just a strange dream of mine)
Burj Khalifa: As the tallest structure in the world, standing at 829.8 meters, Burj Khalifa in Dubai was designed as the centrepiece for a new development called Downtown Dubai. The building was named in honour of the ruler of Dubai and president of the United States Arab Emirates. It was designed by Skidmore, Owings and Merrill (SOM), and the design is inspired by the patterns and structures in Islamic architecture. The structure cost $1.5 billion to build. At the time of its opening in 2010, it had the highest observational deck in the world. The building has even featured in popular culture, as it can be seen in 2016 film, ‘Independence Day: Resurgence’. Burj Khalifa has broken numerous other records, including building with most floors at 211 and it has received immensely positive reception.