There are so many interesting effects of General Relativity which fall in the astrophysical domain. The major ones are gravitational radiation and lensing, black holes and the dynamics of the Universe itself. Gravitational Radiation I'll start with gravitational radiation, since I recently did my physical lab project on it with my lab partner. Put simply, gravitational radiation is generated by accelerating masses, analogous to the generation of electromagnetic waves. However, the two are not exactly the same.
Gravitational waves are quadrupolar in nature.
This is due in part to the conservation of momentum. To explain further, consider a bunch of particles in an isolated region of space. These particles can be doing anything they want, however, the nett momentum of the system will remain constant. In contrast, consider the net electric dipole of the system. The electric dipole is the product of the charge of a particle with its position.