Psychoanalytic
Freud but updated - #psychopaths have strong ID, skewed Ego, and damaged or undeveloped Superego. Resulting in short term primal urges and goals being put into action by an ego that has no effective adult superego oversight. So the person may take violent action to address immediate desires. Lacks remorse, guilt, etc normally provided by the superego

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Hare
Factor-1: people born with psychopathy
Factor-2: those created by severe adverse environments.

Hare's various "checklists" are meant to be a practical way to identify psychopathy in the field, and rely heavily on the person's criminal history as diagnostic elements. In Hare's model, it is presumed unlikely that a psychopath makes it to adulthood without leaving a trail of theft, assualt, or murder that show signs of explosive and unplanned behavior

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Clinical
It may surprise you that in the Diagnostic and Statistical Manual (DSM) and the International Classification of Diseases (ICD) used by medical providers, neither #psychopath nor #sociopath are recognized terms. The closest either get are in the Cluster-B Personality Disorders with Antisocial Personality Disorder (APD or ASPD)

APD overlaps with some, but not all, components of #psychopathy and is not an interchangeable term

That creates discomfort between the medical, legal, and social

Anatomical
A ton of research using fMRI and MRI studies on (especially) incarcerated #psychopaths have suggested a number of brain structures that are particularly quiet or active in people diagnosed with #psychopathy compared to control groups.

This is promising as a bridge between APD and Hare and Clinical, and may provide better field tools for diagnosis and help improve treatment methods.

Unfortunately, there is a somewhat incestuous loop between the current diagnostic screening and this

The issue with the Anatomical is that it again relies on carceral samples, and uses somewhat biased diagnostic tools to select who gets scanned (and who doesn't)

This creates a potential for a self-reinforcing loop that increasingly identifies candidates according to a biased dignostic, and then refines the diagnostic using MRI studies derived from that sampling.

Integratory
This is where the most interesting part is for me. For example, where they have renovated Hare's questionnaires, and posited that #psychopaths are born, and that #sociopaths are made by the environment, but that both are not CATEGORICAL, but rather DIMENSIONAL, and composed of several traits, along which people may vary.

An additional approach is to use the highly validated OCEAN scales, and postulate that #psychopathy is just settings on the OCEAN scales.

In this view, #psychopathy might be:

Primary Psychopathy or Factor-1(Grandiose/Manipulative): high Openness, low Conscientiousness, high Extraversion, low Agreeableness, and low Neuroticism (low anxiety)
Secondary Psychopathy or Factor-2 (Impulsive/Irresponsible): low Conscientiousness, low Agreeableness, and high Neuroticism (anxiety, impulsivity)

Unfortunately, what everyone thinks of when they imagine a Factor-1 #psychopath makes the OCEAN get twisted a bit to fit. So maybe not perfect