Updated background on Hilbert 16th problem?

What is the current situation of the second part of the Hilbert 16th problem? What are the most updated news on this problem?

• (from wikipedia) the second part is: The determination of the upper bound for the number of limit cycles in two-dimensional polynomial vector fields of degree $n$ and an investigation of their relative positions – YCor Sep 16 '18 at 21:00
• @Ycor Thank you for adding the tag "limit cycle"! – Ali Taghavi Sep 16 '18 at 21:00
• @YCor and also adding the wikipedia link and editting the title. – Ali Taghavi Sep 16 '18 at 21:01
• Shall we play update the title to optimize the English? “Updated Background on Hilbert’s 16th Problem”? – Anthony Quas Sep 16 '18 at 23:09
• @AnthonyQuas Thanks for your comment. Do you have a suggestion for revision of the title? – Ali Taghavi Sep 17 '18 at 20:55