As people is suggesting here the solution is to find a decent antispam solution on the server side that works on your inbox and then no matter what device you use all is cleaned up.
Usually this kind of solutions have not been available for general consumers, but to enterprise that have access to the email servers and can configure a variety of filters and extensions.
However this situation has changed: I have been recently using SpamPhobia and I am extremely happy with the results.
The solution consists of a set of robots that scans your inbox. Depending on the kind of email provider you use, password may be required, for example for Gmail and Microsoft accounts (i.e. msn, live, hotmail, outlook) you just need to authorize the app. This can be an stopper for some users, for security concerns, although I have read the privacy and terms policy and they look safe, specially considering I am not offering different access that the one my email provider employees already have ....
The antispam solution is totally free, although there is a paid version that cleans more frequently and includes also threat protection (Virus, malware, phishing) and distribution list management, basically allows you to see what lists you are subscribed to, it move them all out of your inbox by default and then you can select which one you are interested.
Although the company looks very young the product is probably one of the best I have tried so far and the best is it looks they are doing quite active developments and have a nice support.
Hope helps.