Deontological ethics, or deontology, is the broad philosophy which values duty and strict obedience to duty. The dominant proponent of deontological ethics was Immanuel Kant, the father of Kantianism and the categorical imperative. Deontology rejects consequences as a measure of morality, instead focusing on fulfillment of duty to a moral code, and it holds that duty to be the only intrinsic good. It is therefore opposed to Consequentialism, which makes judgements based on consequences. Deontology is often associated with Moral absolutism because it upholds absolute moral rules such as the categorical imperative or God's word. The most popular forms of deontology are Divine command theory and Kantianism.
 Types of Deontological Philosophies
 Agent-centered vs Patient-centered
All deontological ethical theories are divided into agent-centered and patient-centered. Agent-centered deontologists focus on keeping one's moral record spotless no matter what the cost and deal mostly with the actions that one performs. Patient-centered deontologists, on the other hand, focus on upholding one's rights, such as independence, and on respecting the rights of others. One popular example of an agent-centered theory is Divine command theory, the theory that morality is whatever God says it is. 
Deontological theories are built around duty. In Divine command theory, that duty is to God. In Kantianism, that duty is to the Categorical imperative, a chosen moral code that one believes should be universally applied. Duty to a social contract means obedience to rules consensually agreed to and democratically amended. Other theories require duty to some variation of an ethical code like Kant's.
 Arguments for
One argument for deontological ethics is that, unlike consequentialism, it is morally undemanding and its laws are absolute and largely non-negotiable, which makes it very easy to live a normal life while still adhering to the philosophy. In consequentialism, almost everything has a moral consequence and is either right, wrong or, worse, a mix; while deontological ethics is very flexible in that regard because most events would be morally neutral if they didn't break or further one's duty. Deontological ethics is also more enforceable because there are clear violations of duty which will be punished by whoever has been wronged, or, in theory, by God. Hence deontologists are known for a disdain, or even total refusal of compromise, summed up with "let justice be done though the heavens fall."
Another argument is that, while we can certainly know an effect knowing its cause, we cannot certainly know a cause knowing its effect. As such, a cause is restricted to its effect, while an effect is not restricted to one cause. That means, we can judge an effect by its cause, but we cannot judge a cause by its effects. Likewise, we can judge an act by its intentions, but not by its effects.
 Arguments against
Deontology is often criticized for its support of unbending obedience at the expense of the original intent of the rules. Often times, duty can lead people to do terribly irrational or immoral things, while consequentialism is far less likely to. Rules often contradict each other, especially in Divine command theory, which leads to the creation of a subjective hierarchy of duties. Reductio ad absurdum of deontology leads to conclusions where deontologists would actually allow any number of horrible things to happen in the name of rigid morality. Kant's Categorical Imperative, on the other hand, is criticized because the instruction to create rules which should be universal is vague and subject to the potentially flawed opinion of anyone using it.