This model has the Optimus video system (integrated Intel graphics card for low-end graphics + an nVidia graphics card for mid-high-end graphics needs). It works fine with bumblebee. Bluetooth doesn't work. It needs non-free firmware. Sound just works; I didn't had to do anything. The webcam image is upside-down. You need to run the applications with "LD_PRELOAD=/usr/lib/i386-linux-gnu/libv4l/v4l1compat.so" in from of them if the image is upside-down. I know that the following are about a different model, but it's very similar, everything applying to U36SD is valid for U36SG as well.

• http://wiki.debian.org/InstallingDebianOn/Asus/U36SD
• https://help.ubuntu.com/community/Asus_U36SD

root@trisquel:~# lspci -nnk
00:00.0 Host bridge [0600]: Intel Corporation 2nd Generation Core Processor Family DRAM Controller [8086:0104] (rev 09)
	Subsystem: ASUSTeK Computer Inc. Device [1043:1327]
	Kernel driver in use: agpgart-intel
00:01.0 PCI bridge [0604]: Intel Corporation Xeon E3-1200/2nd Generation Core Processor Family PCI Express Root Port [8086:0101] (rev 09)
	Kernel driver in use: pcieport
	Kernel modules: shpchp
00:02.0 VGA compatible controller [0300]: Intel Corporation 2nd Generation Core Processor Family Integrated Graphics Controller [8086:0126] (rev 09)
	Subsystem: ASUSTeK Computer Inc. Device [1043:2111]
	Kernel driver in use: i915
	Kernel modules: i915
00:16.0 Communication controller [0780]: Intel Corporation 6 Series/C200 Series Chipset Family MEI Controller #1 [8086:1c3a] (rev 04)
	Subsystem: ASUSTeK Computer Inc. Device [1043:1327]
	Kernel driver in use: mei
	Kernel modules: mei
00:1a.0 USB controller [0c03]: Intel Corporation 6 Series/C200 Series Chipset Family USB Enhanced Host Controller #2 [8086:1c2d] (rev 05)
	Subsystem: ASUSTeK Computer Inc. Device [1043:1327]
	Kernel driver in use: ehci_hcd
00:1b.0 Audio device [0403]: Intel Corporation 6 Series/C200 Series Chipset Family High Definition Audio Controller [8086:1c20] (rev 05)
	Subsystem: ASUSTeK Computer Inc. Device [1043:1ba3]
	Kernel driver in use: HDA Intel
	Kernel modules: snd-hda-intel
00:1c.0 PCI bridge [0604]: Intel Corporation 6 Series/C200 Series Chipset Family PCI Express Root Port 1 [8086:1c10] (rev b5)
	Kernel driver in use: pcieport
	Kernel modules: shpchp
00:1c.1 PCI bridge [0604]: Intel Corporation 6 Series/C200 Series Chipset Family PCI Express Root Port 2 [8086:1c12] (rev b5)
	Kernel driver in use: pcieport
	Kernel modules: shpchp
00:1c.3 PCI bridge [0604]: Intel Corporation 6 Series/C200 Series Chipset Family PCI Express Root Port 4 [8086:1c16] (rev b5)
	Kernel driver in use: pcieport
	Kernel modules: shpchp
00:1c.5 PCI bridge [0604]: Intel Corporation 6 Series/C200 Series Chipset Family PCI Express Root Port 6 [8086:1c1a] (rev b5)
	Kernel driver in use: pcieport
	Kernel modules: shpchp
00:1d.0 USB controller [0c03]: Intel Corporation 6 Series/C200 Series Chipset Family USB Enhanced Host Controller #1 [8086:1c26] (rev 05)
	Subsystem: ASUSTeK Computer Inc. Device [1043:1327]
	Kernel driver in use: ehci_hcd
00:1f.0 ISA bridge [0601]: Intel Corporation HM65 Express Chipset Family LPC Controller [8086:1c49] (rev 05)
	Subsystem: ASUSTeK Computer Inc. Device [1043:1327]
	Kernel modules: iTCO_wdt
00:1f.2 SATA controller [0106]: Intel Corporation 6 Series/C200 Series Chipset Family 6 port SATA AHCI Controller [8086:1c03] (rev 05)
	Subsystem: ASUSTeK Computer Inc. Device [1043:1327]
	Kernel driver in use: ahci
	Kernel modules: ahci
00:1f.3 SMBus [0c05]: Intel Corporation 6 Series/C200 Series Chipset Family SMBus Controller [8086:1c22] (rev 05)
	Subsystem: ASUSTeK Computer Inc. Device [1043:1327]
	Kernel modules: i2c-i801
01:00.0 VGA compatible controller [0300]: NVIDIA Corporation Device [10de:105a] (rev a1)
	Subsystem: ASUSTeK Computer Inc. Device [1043:2111]
	Kernel modules: nouveau, nvidiafb
03:00.0 Network controller [0280]: Atheros Communications Inc. AR9285 Wireless Network Adapter (PCI-Express) [168c:002b] (rev 01)
	Subsystem: AzureWave AW-NB037H 802.11bgn Wireless Half-size Mini PCIe Card [AR9002WB-1NGCD] [1a3b:2c37]
	Kernel driver in use: ath9k
	Kernel modules: ath9k
05:00.0 Ethernet controller [0200]: Atheros Communications Inc. AR8151 v2.0 Gigabit Ethernet [1969:1083] (rev c0)
	Subsystem: ASUSTeK Computer Inc. Device [1043:1851]
	Kernel driver in use: atl1c
	Kernel modules: atl1c

root@trisquel:~# lsusb 
Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub
Bus 002 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub
Bus 001 Device 002: ID 8087:0024 Intel Corp. Integrated Rate Matching Hub
Bus 002 Device 002: ID 8087:0024 Intel Corp. Integrated Rate Matching Hub
Bus 001 Device 003: ID 0cf3:3005 Atheros Communications, Inc. AR3011 Bluetooth
Bus 001 Device 004: ID 04f2:b1b9 Chicony Electronics Co., Ltd 
Bus 002 Device 003: ID 1687:3257 Kingmax Digital Inc.