public class FollowCamera : MonoBehaviour {
    public GameObject target;
    public float damping = 1;
    Vector3 offset;

    void Start() {
        offset = target.transform.position - transform.position;
    }

    void LateUpdate() {
        float currentAngle = transform.eulerAngles.y;
        float desiredAngle = target.transform.eulerAngles.y;
        float angle = Mathf.LerpAngle(currentAngle, desiredAngle, Time.deltaTime * damping);

        Quaternion rotation = Quaternion.Euler(0, angle, 0);
        transform.position = target.transform.position - (rotation * offset);

        transform.LookAt(target.transform);
    }
}