Why is OnTriggerEnter not called when my objects do not have Rigidbodies?

Question

I am trying to get my enemy to take damage, however it is not working. I know the reason: the box colliders on not triggering the OnTriggerEnter message. I do not know why. Here is my code:

using UnityEngine;

public class EnemyBaseScript : MonoBehaviour
{
    public float health;   
    private Weapon weaponGettingHitBy;

    private void OnTriggerEnter(Collider col)
    {
        Debug.Log("OnTriggerEnter was called");
        if (col.gameObject.CompareTag("Weapon"))
        {
            weaponGettingHitBy = new Weapon(
               col.gameObject, 
               col.gameObject.GetComponent<WeaponBaseScript>().damageDealing
            );            
            health -= weaponGettingHitBy.damageDealt;

            Debug.Log("Took damage from weapon.");
        }   
    }
}

The code for weapons

using UnityEngine;

public class WeaponBaseScript : MonoBehaviour
{
    public float damageDealing;
}

Images of the box colliders:

(I know that some of the box colliders are off it is because I was testing around, assume all are enabled)

Answer 1

As you can see from the Collision action matrix in the documentation:

Trigger messages are sent upon collision

	Static Collider	Rigidbody Collider	Kinematic Rigidbody Collider	Static Trigger Collider	Rigidbody Trigger Collider	Kinematic Rigidbody Trigger Collider
Static Collider					Y	Y
Rigidbody Collider				Y	Y	Y
Kinematic Rigidbody Collider				Y	Y	Y
Static Trigger Collider		Y	Y		Y	Y
Rigidbody Trigger Collider	Y	Y	Y	Y	Y	Y
Kinematic Rigidbody Trigger Collider	Y	Y	Y	Y	Y	Y

In order to generate an OnTriggerEnter(Collider other) message, at least one of the colliders involved has to have the isTrigger flag set, and at least one of the objects involved has to have a Rigidbody attached (either at the same level or in one of its parents).

Colliders with no Rigidbody are considered "static" - the engine expects they will not move, and so it does not check for collisions between them. You should always use a Rigidbody on physics colliders that you will be moving. If you don't want the physics engine to integrate their velocity automatically, use the kinematic mode so you can keep full control of their movement while still getting collision checking.