By the end of the second decade of the 21st century, due to domestic and international developments, Russia and the West entered a state of tensions and a new cycle of the arms race - unprecedented since the worst times of the Cold War. Both sides got into this phase of relationship under the new world order, with advanced military technologies and under the rule of a new generation of political leaders. The turning point of these dangerous trends came with the decision of the United States to withdraw from the INF Treaty and high probability of the expiration of the New START without its extension or substitution by a follow-on treaty after 2021. Hence, the U.S. and Russia are on the verge of a new large-scale and uncontrolled nuclear arms race, which will be aggravated by the rivalry in offensive and defensive conventional strategic and medium range systems, as well as space weapons and means of cyber warfare. In combination with the development and deployment of short-flight-time ballistic and hypersonic systems as well as introduction of low-yield strategic and tactical nuclear arms for "limited" and "tailored" nuclear attacks this would drastically lower nuclear use threshold and increase incentives for preventive or preemptive nuclear strikes. In addition, the arms race will be multilateral, involving, beside the U.S. and Russia, China and many other nations. This would undercut the norms and regimes of nuclear non-proliferation, security and safety of nuclear materials, technologies and sites, which sooner or later would provide international terrorism with the access to nuclear weapons - with all the ensuing consequences. This article is dedicated to the above dangers and still remaining possibilities of averting them. In particular, if the two sides agreed on the new intrusive verification procedures, the INF Treaty still could be saved. Likewise, extension of the New START might stabilize strategic relations for another five years after its expiration in 2021. During those years or, still better, during two years remaining till 2021, a follow-on treaty could be negotiated to reduce strategic arms ceilings and envelop advanced destabilizing nuclear and conventional weapons.