Parameterized hardness:

1) Daniel Marx: Can You Beat Treewidth? Theory of Computing 6(1): 85-112 (2010)
2) Daniel Lokshtanov, Daniel Marx, Saket Saurabh: Slightly Superexponential Parameterized Problems. SIAM J. Comput. 47(3): 675-702 (2018)
3) Daniel Lokshtanov, Daniel Marx, Saket Saurabh: Known Algorithms on Graphs of Bounded Treewidth Are Probably Optimal. ACM Trans. Algorithms 14(2): 13:1-13:30 (2018)
4) Daniel Marx: On the Optimality of Planar and Geometric Approximation Schemes. FOCS 2007: 338-348
5) Daniel Marx: Parameterized Complexity of Independence and Domination on Geometric Graphs. IWPEC 2006: 154-165
6) Bingkai Lin: The Parameterized Complexity of the k-Biclique Problem. J. ACM 65(5): 34:1-34:23 (2018)
7) Michael Lampis: Model Checking Lower Bounds for Simple Graphs. ICALP (1) 2013: 673-683

Complexity theory:

8) Marco Cesati: The Turing way to parameterized complexity. J. Comput. Syst. Sci. 67(4): 654-685 (2003)

Exact algorithms:

9) Fedor V. Fomin, Serge Gaspers, Daniel Lokshtanov, Saket Saurabh: Exact Algorithms via Monotone Local Search. J. ACM 66(2): 8:1-8:23 (2019)
10) Marek Cygan, Holger Dell, Daniel Lokshtanov, Daniel Marx, Jesper Nederlof, Yoshio Okamoto, Ramamohan Paturi, Saket Saurabh, Magnus Wahlstrom:
On Problems as Hard as CNF-SAT. ACM Trans. Algorithms 12(3): 41:1-41:24 (2016)
11) Fedor V. Fomin, Fabrizio Grandoni, Artem V. Pyatkin, Alexey A. Stepanov:
Combinatorial bounds via measure and conquer: Bounding minimal dominating sets and applications. ACM Trans. Algorithms 5(1): 9:1-9:17 (2008)
12) Ioannis Koutis: Faster Algebraic Algorithms for Path and Packing Problems. ICALP (1) 2008: 575-586
13) Ryan Williams: Finding paths of length k in O*(2k) time. Inf. Process. Lett. 109(6): 315-318 (2009)
14) Andreas Bjorklund: Determinant Sums for Undirected Hamiltonicity. FOCS 2010: 173-182
15) Jesper Nederlof: Fast Polynomial-Space Algorithms Using Inclusion-Exclusion. Algorithmica 65(4): 868-884 (2013)
16) Noga Alon, Gregory Z. Gutin, Eun Jung Kim, Stefan Szeider, Anders Yeo: Solving MAX-r-SAT Above a Tight Lower Bound. Algorithmica 61(3): 638-655 (2011)
17) Russell Impagliazzo, Ramamohan Paturi: On the Complexity of k-SAT. J. Comput. Syst. Sci. 62(2): 367-375 (2001)
18) Russell Impagliazzo, Ramamohan Paturi, Francis Zane: Which Problems Have Strongly Exponential Complexity? J. Comput. Syst. Sci. 63(4): 512-530 (2001)

Bidimensionality:

19) Fedor V. Fomin, Daniel Lokshtanov, Saket Saurabh, Dimitrios M. Thilikos: Bidimensionality and Kernels. SODA 2010: 503-510
20) Fedor V. Fomin, Daniel Lokshtanov, Saket Saurabh: Bidimensionality and geometric graphs. SODA 2012: 1563-1575
21) Erik D. Demaine, MohammadTaghi Hajiaghayi: The Bidimensionality Theory and Its Algorithmic Applications. Comput. J. 51(3): 292-302 (2008)

Parameterized subexponential algorithms and square-root phenomenon:

22) Daniel Marx, Michal Pilipczuk: Optimal Parameterized Algorithms for Planar Facility Location Problems Using Voronoi Diagrams. ESA 2015: 865-877
23) Daniel Marx, Marcin Pilipczuk, Michal Pilipczuk: On Subexponential Parameterized Algorithms for Steiner Tree and Directed Subset TSP on Planar Graphs. FOCS 2018: 474-484
24) Fedor V. Fomin, Daniel Lokshtanov, Daniel Marx, Marcin Pilipczuk, Michal Pilipczuk, Saket Saurabh:
Subexponential Parameterized Algorithms for Planar and Apex-Minor-Free Graphs via Low Treewidth Pattern Covering. FOCS 2016: 515-524
25) Fedor V. Fomin, Daniel Lokshtanov, Fahad Panolan, Saket Saurabh, Meirav Zehavi: Decomposition of Map Graphs with Applications. ICALP 2019: 60:1-60:15
26a) Fahad Panolan, Saket Saurabh, Meirav Zehavi: Contraction Decomposition in Unit Disk Graphs and Algorithmic Applications in Parameterized Complexity. SODA 2019: 1035-1054

Treewidth:

26b) Hans L. Bodlaender, Pal Gronas Drange, Markus S. Dregi, Fedor V. Fomin, Daniel Lokshtanov, Michal Pilipczuk: An O(c^k n) 5-Approximation Algorithm for Treewidth. FOCS 2013: 499-508
27) Marek Cygan, Jesper Nederlof, Marcin Pilipczuk, Michal Pilipczuk, Johan M. M. van Rooij, Jakub Onufry Wojtaszczyk: Solving Connectivity Problems Parameterized by Treewidth in Single Exponential Time. FOCS 2011: 150-159

Cut problems:

28) R. H. Chitnis, M. Cygan, M. Hajiaghayi, Ma. Pilipczuk, Mi. Pilipczuk: Designing FPT Algorithms for Cut Problems Using Randomized Contractions. FOCS 2012: 460-469
29) Marek Cygan, Daniel Lokshtanov, Marcin Pilipczuk, Michal Pilipczuk, Saket Saurabh: Minimum Bisection Is Fixed-Parameter Tractable. SIAM J. Comput. 48(2): 417-450 (2019)

LP-based:

30) Yoichi Iwata, Magnus Wahlstrom, Yuichi Yoshida: Half-integrality, LP-branching, and FPT Algorithms. SIAM J. Comput. 45(4): 1377-1411 (2016)
31) Yoichi Iwata, Yutaro Yamaguchi, Yuichi Yoshida: 0/1/All CSPs, Half-Integral A-Path Packing, and Linear-Time FPT Algorithms. FOCS 2018: 462-473

FPT approximations:

32) Michael Lampis: Parameterized Approximation Schemes Using Graph Widths
33) Daniel Lokshtanov, M. S. Ramanujan, Saket Saurabh, Meirav Zehavi: Parameterized Complexity and Approximability of Directed Odd Cycle Transversal. CoRR abs/1704.04249 (2017)
34) Christina Boucher, Christine Lo, Daniel Lokshtanov:
Consensus Patterns (Probably) Has no EPTAS. ESA 2015: 239-250

Logic:

35) Markus Frick, Martin Grohe: Deciding first-order properties of locally tree-decomposable structures. J. ACM 48(6): 1184-1206 (2001)

Kernels, upper bounds:

36) Stephan Thomasse: A 4k2 kernel for feedback vertex set. ACM Trans. Algorithms 6(2): 32:1-32:8 (2010)
37) Bart M. P. Jansen, Astrid Pieterse:
Polynomial Kernels for Hitting Forbidden Minors under Structural Parameterizations. ESA 2018: 48:1-48:15
38) Daniel Lokshtanov, Fahad Panolan, M. S. Ramanujan, Saket Saurabh:
Lossy kernelization. STOC 2017: 224-237
39) Daniel Binkele-Raible, Henning Fernau, Fedor V. Fomin, Daniel Lokshtanov, Saket Saurabh, Yngve Villanger:
Kernel(s) for problems with no kernel: On out-trees with many leaves. ACM Trans. Algorithms 8(4): 38:1-38:19 (2012)
40) Faisal N. Abu-Khzam:
A kernelization algorithm for d-Hitting Set. J. Comput. Syst. Sci. 76(7): 524-531 (2010)
41) Stefan Kratsch, Magnus Wahlstrom: Representative Sets and Irrelevant Vertices: New Tools for Kernelization. FOCS 2012: 450-459

Kernels, lower bounds:

42) Michael Dom, Daniel Lokshtanov, Saket Saurabh:
Kernelization Lower Bounds Through Colors and IDs. ACM Trans. Algorithms 11(2): 13:1-13:20 (2014)
43) Holger Dell, Dieter van Melkebeek:
Satisfiability Allows No Nontrivial Sparsification unless the Polynomial-Time Hierarchy Collapses. J. ACM 61(4): 23:1-23:27 (2014)
44) Holger Dell, Daniel Marx:
Kernelization of packing problems. SODA 2012: 68-81
45) Stefan Kratsch, Geevarghese Philip, Saurabh Ray: Point Line Cover: The Easy Kernel is Essentially Tight. ACM Trans. Algorithms 12(3): 40:1-40:16 (2016)