Articulate the main features of the logical problem of evil and the main objection raised against it. Articulate the main features of the evidential problem of evil and what's required by a theist to address it.

The problem of evil is not just one main problem but several arguments grouped together against the existence of God. Thus, it is a concept present in ethics, philosophy, theism, theology, and religion (mainly the monotheistic religions like Christianity, Judaism and Islam, but it is also characteristic of Budhaism and Hinduism).
A theist would claim that an omnipotent, omniscient, and omnibenevolent God certainly exists. Ironically, the problem of evil uses precisely this claim as evidence against the existence of such a God. Thus, a theologian or a philosopher would ask the question: if an all-knowing, all-seeing, and perfectly good and infinitely benevolent being such as God (or other supreme deity) truly exists, and has power over the entire universe, than why does he/she/it allow evil in its most basic and complicated forms to exist as well?
There are two main types or forms of the problem of evil: the logical problem of evil and the evidental problem of evil.
According to the logical problem of evil, the existence of God is "logically incompatible" with the existence of an omnipotent, omniscient, and omnibenevolent God or deity. Thus, his/her/its existence is impossible. Basically, the argument is that a perfectly and maximally good, kind, rational, all-seeing, and all-knowing God exists, and evil (be it natural or human, necessary or unnecessary) does not; however, evil exists; therefore, God does not.
Here, we are presented with a valid logical argument. If God was not completely omnipotent, omniscient and omnibenevolent, then this logical problem would be resolved. This claim basically defines the evidental (probabilistic) problem of evil; an all-knowing, all-seeing, and wholly and infinitely good God would and should not allow the existence of evil; evil undoubtedly exists; therefore God is definitely not wholy and completely omnipotent, omniscient and omnibenevolent. Thus, the presence of evil is used as evidence against the theistic claim that such a deity truly exists.
The main responses and objections against both the logical and the evidental problem of evil are either refutations, defenses, or theodicies. One commonly used response is that God has justifiable moral and ethical reasons that we do not understand for allowing evil to exist; in other words, he allows pain and suffering to exist for the greater good. However, many philosophers have pointed out that there are numerous instances of all kinds of evil happening in the universe, which have had no good consequences whatsoever. Furthermore, if we do not understand God's reasons, then perhaps there is no justifiable reason at all for God to allow evil to exist.
Another common response is the notion of free will. Here, the claim is that some evil exists because God must allow humans to have free will. Finally, the third most common response is known as the soul-making theodicy. This means that evil exists because it is the best way for people to develop and learn.