OTL amps are a subject I really can get excited about in this hobby.
Advantages include, top to bottom clarity, resolution and tonal naturalness more akin to real music. The reason being there is no transformer that CAN add or detract from the signal. These amps when matched properly to the speaker they will be used with can take you to sonic nirvana like no other amplifying device I have heard including transformer coupled tubes, SET with transformers which typically don't offer the frequency extension of the best OTL designs and ss which with few exceptions doesn't offer the immediacy and presence that seems exclusive to tubes. So the best way to describe OTL's are the best world of both tubes and ss with few if any of the weaknesses with the possible exception of bass "slam" which seems more exclusive to ss designs. Bass resolution and natural impact is of much greater interest to me and is harder to get right than slam (dynamic impact, often exaggerated).
Disadvantages of OTL's are as long listed as their advantages:
Since the output tubes provide all the current to drive the speakers without use of an output transformer, it is important that the impedance characteristics not drop below 4 ohms in any case and ideally should be between 8 and 16 ohms at all frequencies without compromising the performance they are capable of. Unfortunately there are few speakers with these characteristics so use of an OTL is not ideal in most instances. Heat is another problem. They run very hot because many tubes are used in parallel to produce the current necessary. They can be designed for high watts but the price is many tubes and a lot of heat, up to 1,500-2,000 watts for a big pair of mono's.
Dependability has always been an issue with these designs but it seems this has become less so with current designs than in the past. The players include Transcendent, Atmas-phere, Joule, Tenor, Graff and the Berning Quasi OTL. They are all great performers with the right speakers.