According to the Radicati report, in 2015 the number of business and consumer emails sent and received per day was over 205 billion, and in 2017 it will reach 269 billion, “and it is expected to continue to grow at an average annual rate of 4.4% over the next four years, reaching 319.6 billion by the end of 2021”.
Nothing can replace email, but you can change the way you use it and make yourself less email-dependent.
Email can be annoying or even unbearable when it's used as a messaging system. You can mitigate that problem by limiting the times you use it.