How do fat cells work?

When people have liposuction, a lot of the fat is extracted during surgery. But a lot of times you see people gaining weight back. Does the body produce new fat cells? 

When you lose weight naturally through a change of diet and/or exercise, do fat cells shrink or do they disappear? So say a 300 lb person reached 180lb and was steady at that weight for a year. Would the fat cells disappear, or are they still there but "deflated" as there is less overall fat in the body? 
During infancy and adolescence, adipose tissue is growing by a combination of increase in fat cell size (to a lesser extent) and (above all) the number of these cells [1]. In adults, fat cell number is constant over time in spite of a large turnover (about 10% of the fat cells per year) when body weight is stable [1] [2]. A decrease in body weight only changes fat cell size (becoming smaller), whereas an increase in body weight causes elevation of both fat cell size and number in adults [1]. An important source of renewal of fat cells during the entire life span is the bone marrow [1]. There is also a rapid turnover of fat cell lipids, which constitute a single active pool and are renewed about 6 times during the life span of individual fat cells [1]. Overweight and obesity are associated with decreased lipid turnover due to high input in combination with low output of lipids from the fat cells [1]. Scientists still aren't sure why some people have more fat cells than others [3].
The number of fat cells in the body does not change after puberty, and fat cells do not generate after puberty. [1] Rather, the number of fat cells remains the same as the body stores more fat, and the fat cells grow larger or smaller based on weight gain or weight loss. [1, 3] The cells are able to regrow if you lose weight rapidly, such as on a crash diet or intense weight-loss program, because the hormone leptin, which regulates appetite, drops as your weight drops. [2] Weight loss is actually attributed to fat cells shrinking, not losing them entirely. [4] Additionally, a plant-based diet rich in grains, fruits, vegetables, nuts, seeds, and beans can help with weight loss. [4]