By classification theory, I mean the branch of model theory in which people aim to extend the original classification theory by Shelah on stable theories by considering other nice properties (simple, NIP, etc. ...) of theories; in other words, I mean the subject that this Web site is all about. (Is the area really called classification theory?)

I am looking for a survey in this field, so I can read it to assess my interest in the field (I don't know anything about anything about it!) I am aware of a few textbooks/materials about a specific nice property of theories. But I would rather read a survey that encompasses the entire field, explaining the history, motivation, important techniques, and recent trends and results.

Is there such a survey? Unfortunately, the words model, classification and theory are horrendously generic and they are not friendly to search engines.

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    $\begingroup$ This nice survey by Bradd Hart starts with uncountably categorical theories and discusses the generalization of techniques developed there to stable and simple theories. This is not really what you're looking for, since it does not discuss the relationship to the zoo of other dividing lines (NIP, NTP2 and NTP1, NSOP1, NSOP3, etc) - but work on these properties is much more recent, and I'm not aware of a good survey (except maybe for the introduction sections of some papers in the area). $\endgroup$ – Alex Kruckman Mar 5 '17 at 3:41
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    $\begingroup$ This area is sometimes called "neostability theory", though I'm not sure how widely the name has caught on. $\endgroup$ – Alex Kruckman Mar 5 '17 at 3:47
  • $\begingroup$ Whatever it is called, it is definitely not "classification theory". All unstable (actually unsuperstable) theories have the maximum number of models in uncountable cardinalities. So the classes of their models can't be classified. $\endgroup$ – Levon Haykazyan Mar 5 '17 at 23:43
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    $\begingroup$ @LevonHaykazyan Aptly or not, some people definitely still call it classification theory. $\endgroup$ – Mike Haskel Mar 6 '17 at 2:04
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    $\begingroup$ Ironically, the name classification theory still seems appropriate - but in the sense of classifying theories by complexity, not classifying their models! $\endgroup$ – Alex Kruckman Mar 6 '17 at 13:39

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