What are the must-read search trees paper? I would like to ask a help from researchers who conduct a research in an area of search trees. Could you please write the list of the must-read papers and most recent papers which are important to read
if I want to write papers about search trees.

I personally has the following list of papers (It's nonuniform, quite old and affects different topics. There is also a huge amount of papers about finger search tree but I didn't write references to them).
Thank you for help. 


Daniel Dominic Sleator and Robert Endre Tarjan. 1985. Self-adjusting binary search trees. J. ACM 32, 3 (July 1985), 652-686. DOI=http://dx.doi.org/10.1145/3828.3835
Daniel D. Sleator and Robert Endre Tarjan. 1983. A data structure for dynamic trees. J. Comput. Syst. Sci. 26, 3 (June 1983), 362-391. DOI=http://dx.doi.org/10.1016/0022-0000(83)90006-5
Scott Huddleston and Kurt Mehlhorn. 1982. A new data structure for representing sorted lists. Acta Inf. 17, 2 (June 1982), 157-184. DOI=http://dx.doi.org/10.1007/BF00288968
Erik D. Demaine, Dion Harmon, John Iacono, Daniel Kane, and Mihai Pătraşcu. 2009. The geometry of binary search trees. In Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '09). Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 496-505.
Samuel W. Bent, Daniel D. Sleator, and Robert E. Tarjan. Biased Search Trees. SIAM Journal on Computing 1985 14:3, 545-568
Parinya Chalermsook, Mayank Goswami, László Kozma, Kurt Mehlhorn, Thatchaphol Saranurak:
Self-Adjusting Binary Search Trees: What Makes Them Tick? ESA 2015: 300-312


Since I conducted research in area of fast concatenation of search trees:


Haim Kaplan and Robert E. Tarjan. 1996. Purely functional representations of catenable sorted lists. In Proceedings of the twenty-eighth annual ACM symposium on Theory of computing (STOC '96). ACM, New York, NY, USA, 202-211. DOI=http://dx.doi.org/10.1145/237814.237865
Purely Functional Worst Case Constant Time Catenable Sorted Lists. Lecture Notes in Computer Science.  Gerth Stølting Brodal, Christos Makris, and Kostas Tsichlas.  Algorithms – ESA 2006, Chapter 18, 172-183. Berlin, Heidelberg.  http://link.springer.com/10.1007/11841036_18
Sleator-Tarjan '85 and Demaine et al '09 definitely belong on any such list.
There is a lot of other recent work related to splay trees and dynamic optimality, for instance:


Applications of forbidden 0-1 matrices to search tree and path compression-based data structures, Seth Pettie, SODA 2010
An O (log log n)-competitive binary search tree with optimal worst-case access times, Bose et al, SWAT 2010
Upper bounds for maximally greedy binary search trees, Kyle Fox, WADS 2011.
De-amortizing binary search trees, Bose et al, ICALP 2012
Pattern-avoiding access in binary search trees, Chalermsook et al, FOCS 2015
Weighted dynamic finger in binary search trees, Iacono and Langerman, SODA 2016


On more classical lines, I think


Rank-balanced trees, Haeupler, Sen, and Tarjan, ACM TALG 2015


is worth including as an elegant unification of AVL and red-black trees.