Quasi-linear systems of partial differential equations include Einstein's systems of equations of general relativity, systems of conservation laws, and variational wave equations of liquid crystals. Solutions to these systems of equations may be singular, and usually their blow-ups depend on the physical parameters. I will briefly mention recent results in this area, and give a no-blow-up condition. Also, I construct  a global energy conservative weak solution after blow-up. These are joint works with Professor Yuxi Zheng.