For the first 1.5 billion years, prokaryotes ruled the earth (and still do). It was not until about 2,100 million years ago that the first eukaryote evolved. It is hypothesised that the first eukaryote was a result of a larger prokaryote engulfing a smaller prokaryote (symbiosis) and they began to cohabitate together. The evidence for this is that mitochondrian and chlorophylls have their own DNA and are very similar to prokaryotic cells.
All cells are surrounded by a plasma membrane of some kind, but depending on the cell type they can also be surrounded by additional structures. Plant cells have a cell wall to maintain hydrostatic pressure and gram-positive bacteria have a thick coating of peptidoglycans surrounding their plasma membrane.