Deterrence theory
It states that when two countries each have nuclear weapons, the probability of a direct war between them greatly decreases, but the probability of minor or indirect conflicts between them increases. This occurs because rational actors want to avoid nuclear wars, and thus they neither start major conflicts nor allow minor conflicts to escalate into major conflicts—thus making it safe to engage in minor conflicts. For instance, during the Cold War the United States and the Soviet Union never engaged each other in warfare, but fought proxy wars in Korea, Vietnam, Angola, the Middle East, Nicaragua and Afghanistan and spent substantial amounts of money and manpower on gaining relative influence over the third world.
Bernard Brodie wrote in 1959 that a credible nuclear deterrent must be always ready but never used.
Scholars have debated whether having a superior nuclear arsenal provides a deterrent against other nuclear-armed states with smaller arsenals. Matthew Kroenig has argued that states with nuclear superiority are more likely to win nuclear crises, whereas Todd Sechser, Matthew Fuhrmann and David C. Logan have challenged this assertion. A 2023 study found that a state with nuclear weapons is less likely to be targeted by non-nuclear states, but that a state with nuclear weapons is not less likely to target other nuclear states in low-level conflict. A 2022 study by Kyungwon Suh suggests that nuclear superiority may not reduce the likelihood that nuclear opponents will initiate nuclear crises.
Proponents of nuclear deterrence theory argue that newly nuclear-armed states may pose a short- or medium-term risk, but that "nuclear learning" occurs over time as states learn to live with new nuclear-armed states. Mark S. Bell and Nicholas L. Miller have however argued that there is a weak theoretical and empirical basis for notions of "nuclear learning."

Stages of US policy of deterrence: The US policy of deterrence during the Cold War underwent significant variations.

Containment: The early stages of the Cold War were generally characterized by the containment of communism, an aggressive stance on behalf of the US especially on developing nations under its sphere of influence. The period was characterized by numerous proxy wars throughout most of the globe, particularly Africa, Asia, Central America, and South America. One notable conflict was the Korean War. George F. Kennan, who is taken to be the founder of this policy in his Long Telegram, asserted that he never advocated military intervention, merely economic support, and that his ideas were misinterpreted as espoused by the general public.

Détente: With the US drawdown from Vietnam, the normalization of US relations with China, and the Sino-Soviet Split, the policy of containment was abandoned and a new policy of détente was established, with peaceful co-existence was sought between the United States and the Soviet Union. Although all of those factors contributed to this shift, the most important factor was probably the rough parity achieved in stockpiling nuclear weapons with the clear capability of mutual assured destruction (MAD). Therefore, the period of détente was characterized by a general reduction in the tension between the Soviet Union and the United States and a thawing of the Cold War, which lasted from the late 1960s until the start of the 1980s. The doctrine of mutual nuclear deterrence then characterized relations between the United States and the Soviet Union and relations with Russia until the onset of the New Cold War in the early 2010s. Since then, relations have been less clear.

Reagan era: A third shift occurred with US President Ronald Reagan's arms build-up during the 1980s. Reagan attempted to justify the policy by concerns of growing Soviet influence in Latin America and the post-1979 revolutionary government of Iran. Similar to the old policy of containment, the US funded several proxy wars, including support for Saddam Hussein of Iraq during the Iran–Iraq War, support for the mujahideen in Afghanistan, who were fighting for independence from the Soviet Union, and several anticommunist movements in Latin America such as the overthrow of the Sandinista government in Nicaragua. The funding of the Contras in Nicaragua led to the Iran-Contra Affair, while overt support led to a ruling from the International Court of Justice against the United States in Nicaragua v. United States.
The final expression of the full impact of deterrence during the cold war can be seen in the agreement between Reagan and Mikhail Gorbachev in 1985. They "agreed that a nuclear war cannot be won and must never be fought. Recognizing that any conflict between the USSR and the U.S. could have catastrophic consequences, they emphasized the importance of preventing any war between them, whether nuclear or conventional. They will not seek to achieve military superiority.".
While the army was dealing with the breakup of the Soviet Union and the spread of nuclear technology to other nations beyond the United States and Russia, the concept of deterrence took on a broader multinational dimension. The US policy on deterrence after the Cold War was outlined in 1995 in the document called "Essentials of Post–Cold War Deterrence". It explains that while relations with Russia continue to follow the traditional characteristics of MAD, but the US policy of deterrence towards nations with minor nuclear capabilities should ensure by threats of immense retaliation (or even pre-emptive action) not to threaten the United States, its interests, or allies. The document explains that such threats must also be used to ensure that nations without nuclear technology refrain from developing nuclear weapons and that a universal ban precludes any nation from maintaining chemical or biological weapons. The current tensions with Iran and North Korea over their nuclear programs are caused partly by the continuation of the policy of deterrence.

Post-Cold War period: By the beginning of the 2022 Russian invasion of Ukraine, many western hawks expressed the view that deterrence worked in that war but  only in one way – in favor of Russia. Former US security advisor, John Bolton, said: Deterrence is working in the Ukraine crisis, just not for the right side. The United States and its allies failed to deter Russia from invading. The purpose of deterrence strategy is to prevent the conflict entirely, and there Washington failed badly. On the other hand, Russian deterrence is enjoying spectacular success. Russia has convinced the West that even a whisper of NATO military action in Ukraine would bring disastrous consequences. Putin threatens, blusters, uses the word “nuclear,” and the West wilts.
When Elon Musk prevented Ukraine from carrying drone attacks on the Russian Black Sea fleet by denying to enable needed Starlink communications in Crimea, Anne Applebaum argued Musk had been deterred by Russia after the country's ambassador warned him an attack on Crimea would be met with a nuclear response. Later Ukrainian attacks on the same fleet using a different communications system also caused deterrence, this time to the Russian Navy.
Timo S. Koster who served at NATO as Director of Defence Policy & Capabilities similarly argued: A massacre is taking place in Europe and the strongest military alliance in the world is staying out of it. We are deterred and Russia is not. Philip Breedlove, a retired four-star U.S. Air Force general and a former SACEUR, said that Western fears about nuclear weapons and World War III have left it "fully deterred" and Putin "completely undeterred." The West have "ceded the initiative to the enemy." No attempt was made by NATO to deter Moscow with the threat of military force, wondered another expert. To the contrary, it was Russia’s deterrence that proved to be successful.

Cyber deterrence: Since the early 2000s, there has been an increased focus on cyber deterrence. Cyber deterrence has two meanings:

The use of cyber actions to deter other states
The deterrence of an adversary's cyber operations
Scholars have debated how cyber capabilities alter traditional understandings of deterrence, given that it may be harder to attribute responsibility for cyber attacks, the barriers to entry may be lower, the risks and costs may be lower for actors who conduct cyber attacks, it may be harder to signal and interpret intentions, the advantage of offense over defense, and weak actors and non-state actors can develop considerable cyber capabilities. Scholars have also debated the feasibility of launching highly damaging cyber attacks and engaging in destructive cyber warfare, with most scholars expressing skepticism that cyber capabilities have enhanced the ability of states to launch highly destructive attacks. The most prominent cyber attack to date is the Stuxnet attack on Iran's nuclear program. By 2019, the only publicly acknowledged case of a cyber attack causing a power outage was the 2015 Ukraine power grid hack.
There are various ways to engage in cyber deterrence:

Denial: preventing adversaries from achieving military objectives by defending against them
Punishment: the imposition of costs on the adversary
Norms: the establishment and maintenance of norms that establish appropriate standards of behavior
Escalation: raising the probability that costs will be imposed on the adversary
Entanglement and interdependence: interdependence between actors can have a deterrent effect
There is a risk of unintended escalation in cyberspace due to difficulties in discerning the intent of attackers, and complexities in state-hacker relationships. According to political scientists Joseph Brown and Tanisha Fazal, states frequently neither confirm nor deny responsibility for cyber operations so that they can avoid the escalatory risks (that come with public credit) while also signaling that they have cyber capabilities and resolve (which can be achieved if intelligence agencies and governments believe they were responsible).
According to Lennart Maschmeyer, cyber weapons have limited coercive effectiveness due to a trilemma "whereby speed, intensity, and control are negatively correlated.