The Derg were overthrown in the early 1990s, by an alliance of Eritrean separatists and forces mainly recruited from Tigre. Ethiopia held elections, which were won by the EPRDF (Ethiopian People's Revolutionary Democratic Front, I think), a party led by the Tigrean movement that had defeated the Derg. Eritrea became independent, but at the time it seemed that it would remain forever friends with its large neighbour. Unfortunately, relations between the two countries soured, and a border dispute led to war. In African terms, this war was somewhat unique, in that it saw fighting conducted along a relatively static frontline and was fought mainly by soldiers against other soldiers, rather than against civilians. The war has left a lasting legacy of bitterness between the two countries' governments, and the frontier remains closed. More recently, Ethiopian forces have been deployed in Somalia against the Islamic Courts movement there; Eritrean support for the Islamists has turned this conflict into something of a proxy replay of the Eritrea-Ethiopia war.
Domestically, the rule of the EPRDF have drifted towards more authoritarian rule. Elections in 2005 ended in a shambles when the government announced they had won in a not entirely convincing manner. Protests against this were put down with lethal force, and the entire opposition leadership arrested for a while. Since then, EPRDF figures have talked about how it will take time to build democracy in Ethiopia (perhaps the several hundred years it took to do this in Europe); in any case, some suggest, maybe liberal democracy as seen in the West is not so appropriate for the country. Perhaps related to all this, perhaps not, some areas of the country have seen the re-emergence of ethnic-linguistic-separatist struggles, though these are still somewhat inconsequential.
That makes it sound like Ethiopia is in a lot of trouble at the moment, but that would be an exaggeration. The EPRDF may be creeping towards authoritarianism, but they are not insane maniacs like the Derg or totally rubbish like the later years of the Haile Selaise regime. There are still pressures within the country towards political openness, and the regime has not instituted the kind of full-on authoritarianism that its former allies in Eritrea have. The country remains relatively functional in a way not normally see in sub-Saharan Africa (though I may be in a better position to judge this if I actually go there).
Economically, the country remains heavily focussed on agriculture. Beyond food grown for subsistence or the internal market, coffee is the main cash crop. There is some domestic industry and a growing tourist sector. The country is at the moment experiencing rapid economic growth, but it is unfortunately also suffering from high inflation. Basic foodstuffs in particular are becoming too expensive for the urban poor, pushing them into aid dependency.